Answer:
[tex]6\sqrt{19} \approx 26.153[/tex] inches.
Step-by-step explanation:
The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment [tex]\mathsf{AG}[/tex].
In this diagram (not to scale,) [tex]\mathsf{AB} = 26[/tex] (length of prism,) [tex]\mathsf{AC} = 2[/tex] (width of prism,) [tex]\mathsf{AE} = 2[/tex] (height of prism.)
Pythagorean Theorem can help find the length of [tex]\mathsf{AG}[/tex], one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.
Start by finding the length of line segment [tex]\mathsf{AD}[/tex]. That's the black dotted line in the diagram. In right triangle [tex]\triangle\mathsf{ABD}[/tex] (second diagram,)
Segment [tex]\mathsf{AD}[/tex] is the hypotenuse. One of the legs of [tex]\triangle\mathsf{ABD}[/tex] is [tex]\mathsf{AB}[/tex]. The length of [tex]\mathsf{AB}[/tex] is [tex]26[/tex], same as the length of this prism.Segment [tex]\mathsf{BD}[/tex] is the other leg of this triangle. The length of [tex]\mathsf{BD}[/tex] is [tex]2[/tex], same as the width of this prism.Apply the Pythagorean Theorem to right triangle [tex]\triangle\mathsf{ABD}[/tex] to find the length of [tex]\mathsf{AB}[/tex], the hypotenuse of this triangle:
[tex]\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}[/tex].
Consider right triangle [tex]\triangle \mathsf{ADG}[/tex] (third diagram.) In this triangle,
Segment [tex]\mathsf{AG}[/tex] is the hypotenuse, while[tex]\mathsf{AD}[/tex] and [tex]\mathsf{DG}[/tex] are the two legs.[tex]\mathsf{AD} = \sqrt{26^2 + 2^2}[/tex]. The length of segment [tex]\mathsf{DG}[/tex] is the same as the height of the rectangular prism, [tex]2[/tex] (inches.) Apply the Pythagorean Theorem to right triangle [tex]\triangle \mathsf{ADG}[/tex] to find the length of the hypotenuse [tex]\mathsf{AG}[/tex]:
[tex]\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}[/tex].
Hence, the length of the longest line segment in this prism is [tex]6\sqrt{19} \approx 26.153[/tex] inches.
The longest line segment in a right rectangular prism with dimensions 26 inches by 2 inches by 2 inches is found using the Pythagorean theorem: d = sqrt(l^2 + w^2 + h^2), which gives approximately 26.2 inches.
Explanation:To find the measurement of the longest line segment in a right rectangular prism, we need to calculate the space diagonal, which is the diagonal that cuts through the body of the prism. In this case, the dimensions of the right rectangular prism are 26 inches long, 2 inches wide, and 2 inches tall. We use the Pythagorean theorem in three dimensions to calculate this, which is the square root of the sum of the squares of the length, width, and height. The formula can be written as:
d = \sqrt{l^2 + w^2 + h^2}Where d is the diagonal, l is the length, w is the width, and h is the height. Plugging in the given dimensions:
d = \sqrt{26^2 + 2^2 + 2^2}Calculating the square of each term and adding them gives:
d = \sqrt{676 + 4 + 4}So:
d = \sqrt{684}Finally, taking the square root gives us the length of the longest line segment:
d = 26.2 inchesTherefore, the longest line segment of the rectangular prism measures approximately 26.2 inches.
Which table shows a positive correlation? A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 5, 5, 5, 5, 5. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 10, 18, 31, 37, 52. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 24, 25, 13, 9, 6. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 9, 12, 17, 21, 22.
Answer: The Answer is B
Step-by-step explanation:
The first box has all 5's so it's just going to be a straight line.
The third box is a negative correlation because the number are going down in the right column
The fourth column doesn't make any sense because the X column has all 8's
So the answer is B.
Hope this helps : )
The table shows a positive correlation in B; The first column is labeled x with entries 1, 2, 3, 4, and 5. The second column is labeled y with entries 10, 18, 31, 37, and 52. A 2-column table with 5 rows.
What is correlation?The correlation of two pairs of data values tells about the degree of movement that can occur in one of the data when another data value is increased or decreased respectively.
Since it is called that the Correlation coefficient is a measure of how similar two datasets are acting.
The first box has all 5s =hence, it's just going to be a straight line.
The third box is a negative correlation due to the number is going down in the right column
The fourth column, the X column has all 8's
Hence, the answer is B.
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a) Write down 375 as the product of prime factors.
Give your answer in index form.
b) Work out the highest common factor of 375 and 150.
Answer:
a) 3x5³
b) 75
Step-by-step explanation:
a) find the Prime factors of 375 by dividing your number by prime numbers (you answers must be whole) use a factor tree to help you
a) do the same to 150
one you have you answers in this case we have
375- 3x5x5x5
150 - 2x3x5x5
you collect all the like terms, this will be 3x5x5 then you just simply multiply it And it gives you 75
375 as a product of prime factors is 3x5^3 and the highest common factor of 375 and 150 is 25.
Explanation:To express 375 as the product of prime factors, you must first determine the prime numbers that when multiplied together will equal 375. The prime factors of 375 are 3 and 5. So, 375 can be written as 3x5^3.
Next, to find the highest common factor of 375 and 150, you need to first find the prime factors of both numbers. As shown above, the prime factors of 375 are 3 and 5. The prime factors of 150 are 2, 3 and 5.
The highest common factor is identified by locating the largest number that can divide both numbers without leaving a remainder. The highest common factor of 375 and 150 is hence, 25 because it's the greatest factor that both numbers have in common.
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Find the area of the polygon.
_12 cm
| 19 cm
12 cm
The area of the polygon is |
square centimeters.
Answer:
[tex]A = 1172.965\,cm^{2}[/tex]
Step-by-step explanation:
Let be a side of 12 cm (l) and an apothem of 19 cm (p). First, the number of sides has to be determined:
[tex]n =\frac{360^{\textdegree}}{2\cdot \tan^{-1}\left(\frac{6\,cm}{19\,cm} \right)}[/tex]
[tex]n = 10.271[/tex]
The polygon has ten sides and the side length shall be re-adjusted:
[tex]\theta = \frac{360^{\textdegree}}{10}[/tex]
[tex]\theta = 36^{\textdegree}[/tex]
The side length is:
[tex]l = 2\cdot (19\,cm)\cdot \tan 18^{\textdegree}[/tex]
[tex]l = 12.347\,cm[/tex]
The area of the polygon is:
[tex]A = \frac{n\cdot l \cdot p}{2}[/tex]
[tex]A = \frac{(10)\cdot (12.347\,cm)\cdot (19\,cm)}{2}[/tex]
[tex]A = 1172.965\,cm^{2}[/tex]
is the expression 4 - x the same as x – 4? Explain
Answer:
Yes
Step-by-step explanation:
The order of the factors does not alter the product
Yes because of your property’s
A piece of copper has a mass of 58kg and displaces 5918ml. What is its density?
Answer:
8.96 g/cm2
Step-by-step explanation:
if the volume of a cube is 1,000 cubic feet what is the surface area
Here,
volume(v)=1000 ft^3
also,
v=l^3
or,1000=l^3
therefore,
l=10ft
Now,
Surface area(A)=6l^2
=6×10^2
=600 ft^2
Hope it helps!!!!!
If the volume of a cube is 1,000 cubic feet then the Surface area(A) of a cube of side 10 feet would be 600 ft^2.
What is a cube?A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
The volume of a cube can be calculated as the cube of the sides of a given figure.
The volume of a cube = side ^3
Given ; if the volume of a cube is 1,000 cubic feet
The volume(v) = 1000 ft^3
also, The volume(v) = l^3
or,1000 = l^3
therefore, l = 10ft
The side of the given cube is 10 feet.
Now,
The Surface area(A) of a cube = 6l^2
= 6 × 10^2
= 600 ft^2
Hence, if the volume of a cube is 1,000 cubic feet then the Surface area(A) of a cube of side 10 feet would be 600 ft^2.
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A trapezoid with bases of 18 feet and 12 feet, height of 4 feet, and side length of 5 feet. What statements are true? Check all that apply. The height of the new trapezoid will be 1 ft. The height of the new trapezoid will be 16 ft. The area of the new trapezoid is One-fourth times the area of the original trapezoid. The area of the new trapezoid is StartFraction 1 Over 16 EndFraction times the area of the original trapezoid. The area of the new trapezoid is 4 times the area of the original trapezoid.
Answer:
A and D
Step-by-step explanation:
Got it right :)
Final answer:
The true statement about the new trapezoid is that the area of the new trapezoid is \(1/16\) times the area of the original trapezoid, assuming that all dimensions are scaled down by the same factor.
Explanation:
The area of a trapezoid is given by the formula: [tex]Area = \((base_1 + base_2) / 2\) * height[/tex]. For the original trapezoid with bases of 18 feet and 12 feet and a height of 4 feet, the area is [tex]\((18 + 12) / 2\) * 4 = 60[/tex] square feet. If the dimensions of the trapezoid are scaled down or up, the new height and area can be determined by using the same proportionality principle that applies to triangles. If the height is reduced by a factor of 4, which means the new height is 1 foot, then the area will also be reduced by the same factor squared (since area is a two-dimensional measure). Therefore, the new area will be 1/16 times the original area, which equals 60 / 16 = 3.75 square feet.
The following box plot shows the number of years during which 20 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for 6 years or more?
4 schools
5 schools
10 schools
11 schools
Answer:
B
Step-by-step explanation:
Finish the phrase "Lack of planning on your part doesn't require..." (use all lowercase letter and put spaces between each word).
Help me please !
Its another lock
Answer:
"Lack of planning on your part doesn't require an emergency on my part."
Step-by-step explanation:
Doesnt it say it in the photo?
is 1.6 rational or irrational
0.00005026 as a scientific notation
Answer:
5026*10^-5
Step-by-step explanation:
Answer:
5.026 x 10-5
Step-by-step explanation:
Which expression shows the simplified form of (8 r Superscript negative 5 Baseline) Superscript negative 3?
8 r 15
8/r15
512r 15
r15/512
Answer:
(8r) ^ 15
Step-by-step explanation:
(8r) ^-5 ^-3
We know that a^b^c = a^ (b*c)
(8r) ^-5 ^-3 = (8r) ^ (-5*-3) = (8r) ^ 15
Answer:
This other person is wrong!Step-by-step explanation:
I have proof! Try answer C: or :b
haha smiley face..if not...here's some memes that i hand made....
Trapezoid $RSTU$ is a cross section of a lampshade. The diagonals of $RSTU$ are congruent, and the measure of $\angle S$ is $112\degree$ . What is the measure of $\angle U$ ?
The sum of the angle ∠T and angle ∠U will be a 180°. Then the angle ∠U will be 68°.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
Trapezoid RSTU is a cross-section of a lampshade.
The diagonals of RSTU are congruent, and the measure of angle S is 112 degrees.
Then the measure of angle U will be
Angle S and angle T are equal.
∠S = ∠T = 112°
And the sum of the angle ∠T and angle ∠U will be a 180°.
Then we have
∠T + ∠U = 180°
112° + ∠U = 180°
∠U = 68°
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The measure of angle U in the trapezoid RSTU with congruent diagonals and angle S measuring 112 degrees is 68 degrees, using the properties of an isosceles trapezoid.
To find the measure of in the trapezoid RSTU, with diagonals congruent and the measure of angle S being 112 degrees, we need to use the properties of a trapezoid and the fact that the diagonals are congruent. In an isosceles trapezoid, the base angles are congruent, meaning angles S and U are congruent because diagonals are congruent. Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation: 2(112) + 2(angle U) = 360.
Solving for angle U, we get:
224 + 2(angle U) = 3602(angle U) = 136angle U = 68 degreesHence, the measure of angle U in the trapezoid RSTU is 68 degrees.
Peter ran 4 ⅔ miles on Tuesday. On Wednesday, he ran ⅘ of this distance. How far did he run?
Answer:
3.73333
Step-by-step explanation:
Answer:
Step-by-step explanation:
Distance = 4/5 of 4 2/3
[tex]=\frac{4}{5}*\frac{14}{3}\\\\=\frac{4*14}{5*3}[/tex]
= 56/15
= 3 11/15 miles
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -3 (multiplicity 3) 2(multiplicity 1)and with f(0)=270 .
Final answer:
To write a polynomial f(x) with specified zeros and a value for f(0), we first express the polynomial in its factored form, then solve for the coefficient using the given f(0) value. The resulting polynomial is f(x) = -5(x + 3)^3(x - 2).
Explanation:
To write a polynomial f(x) of the lowest degree with zeros of -3 (multiplicity 3) and 2 (multiplicity 1), we use the fact that zero of multiplicity m means the factor corresponding to that zero will appear m times in the factored form of the polynomial. Given these zeros, the polynomial in its factored form is:
f(x) = a(x + 3)^3(x - 2)
We are also given that f(0) = 270. We can use this information to find the value of a:
f(0) = a(0 + 3)^3(0 - 2) = 270
a = 270 / [(-2)(3)^3]
a = 270 / (-54)
a = -5
Now we can write the polynomial with the determined value of a:
f(x) = -5(x + 3)^3(x - 2)
This is the polynomial of the lowest degree that meets the given conditions.
Rose lives 3/4 of a mile from her cousin. One day she rode her bike to her cousin's house. When she got 2/5 of the way there, her bike chain broke and she had to walk the rest of the way. What part of a mile did Rose go on her bike before it broke?
Answer: 3/10 of a mile
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the 2/5 of the way that she travelled on her bike before it broke by the total distance (3/4 of a mile)
2/5 x 3/4 = 3/10 of a mile
She travelled 3/10 of a mile on her bike before it broke
Feel free to ask for more if needed or if you did not understand something.
Rose traveled [tex]\( \frac{3}{10} \)[/tex] of a mile on her bike before it broke, found by multiplying 2/5 by 3/4. Equation: Distance on bike = (2/5) × (3/4).
To find out what fraction of a mile Rose traveled on her bike before it broke, we need to find 2/5 of 3/4 mile.
[tex]\[ \text{Distance traveled on bike} = \left(\frac{2}{5}\right) \times \left(\frac{3}{4}\right) \][/tex]
[tex]\[ = \frac{2}{5} \times \frac{3}{4} \][/tex]
[tex]\[ = \frac{2 \times 3}{5 \times 4} \][/tex]
[tex]\[ = \frac{6}{20} \][/tex]
[tex]\[ = \frac{3}{10} \][/tex]
So, Rose traveled [tex]\( \frac{3}{10} \)[/tex] of a mile on her bike before it broke.
The equation for this would be:
[tex]\[ \text{Distance on bike} = \left(\frac{2}{5}\right) \times \left(\frac{3}{4}\right) \][/tex]
Complete Question:
Rose lives 3/4 of a mile from her cousin. One day she rode her bike to her cousin's house. When she got 2/5 of the way there, her bike chain broke and she had to walk the rest of the way. What part of a mile did Rose go on her bike before it broke? Show your work and write an EQUATION in the box to the right.
I will comment the other answer choices but help me please
Do I choose A or B?
If so: B
What is the midpoint between (7 - 3i) and ( 3 + 2i).
Answer:
Step-by-step explanation:
5-0.5i
Bree made 48 cookies. She used 1,104 chocolate chips for all of the cookies. How many chocolate chips were in each cookie?
Answer:
23
Step-by-step explanation:
its 23 beacuase 1104 divided by 48 is 23 so its 23 chips
Answer: 23
Step-by-step explanation: 1,104 divided by 48 = 23
Create a rational function with a non-constant denominator) that has NO vertical
asymptotes.
Answer:
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]
Step-by-step explanation:
A rational function with no vertical asymptotes contains an avoidable discontinuity, an example is presented hereafter:
[tex]y = 3[/tex]
[tex]y = 3\cdot 1[/tex]
[tex]y = 3\cdot \frac{x+1}{x+1}[/tex]
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]
(17) Find the least square number which is exactly divisible by each of the numbers
6, 9, 15 and 20.
(18) Find the least square number which is exactly divisible by each of the numbers
8, 12, 15 and 20.
(17) Find the least square number which is exactly divisible by each of the numbers
The answer is 3
(18) Find the least square number which is exactly divisible by each of the numbers
8, 12, 15 and 20.
The answer is 4
Answer:17) 5400
18)3600
Step-by-step explanation:
If a variable does not have a coefficient then it is either a 1 or a -1. true or false
Answer:
True
Step-by-step explanation:
If the coefficient is -1 then the variable will have a negative sign in front of it.
Example: (-x)
If the coefficient is 1 then the variable will stand alone.
Example: (x)
Answer:
True
Step-by-step explanation:
An example of a variable "without" a coefficient is x or -x. There is no number beside x, meaning there is no visible coefficient. And when there is no visible, coefficient, the variable is multiplied by 1 or -1 (the negative sign determines whether the variable is negative or not).
What do the three red tiles in the model of the equation below represent?
2 long x tiles and 3 square 1 tiles = 3 negative x tiles
–3
3
–3x
3x
Answer:
the answer is c
Step-by-step explanation:
Answer:
The answer is -3x because the red tiles represent -x so since there are 3 -x tiles the answer would be -3x
find the edge length of the cube
Answer:
5
Step-by-step explanation:
follow me if I'm right
Answer:
you are wrong genius
Step-by-step explanation:
you are wrong because you might have thought the s is a 5, but it is an s
Steve bought a triangular mat to cover a corner of his room. How much area of the floor will this mat cover?
A. 60 square feet
B. 80 square feet
C. 48 square feet
D. 24 square feet
Please help worth 40 points!
Answer:
i believe is c
Step-by-step explanation:
because you addd 10 plus 8 times 6.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The area of the floor that will be covered by the Matt is 24 sq. ft.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
The area of the floor covering will be equal to the area of the triangular carpet. Therefore, using the Heron's formula we can write,
s = (10+8+6)/2 = 12
Area of the triangle = √[12(12-10)(12-8)(12-6)] = √(12×2×4×6) = 24 sq ft.
Hence, the area of the floor that will be covered by the Matt is 24 sq. ft.
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this is asking using the completing the square method
Answer:
first box [
4
]
second box [
7
____
2
]
third box[
0
]
Step-by-step explanation:
The ratio of the cost of one metre of polyester fabric to the cost of one metre of cotton fabric is 2:7
Complete the table of costs
Answer:
The values of the table of costs in the explanation
Step-by-step explanation:
Let
x ---->the cost of one metre of polyester fabric
y ----> the cost of one metre of cotton fabric
we know that
The ratio of the cost of one metre of polyester fabric to the cost of one metre of cotton fabric is
[tex]\frac{x}{y}=\frac{2}{7}[/tex]
Complete the table
Part 1) For 2 metres of fabric
To find out the costs multiply the ratio by the fraction 2/2
so
[tex](\frac{2}{2})\frac{2}{7}=\frac{4}{14}[/tex]
therefore
[tex]x=\£4\\y=\£14[/tex]
Part 2) For 6 metres of fabric
To find out the costs multiply the ratio by the fraction 6/6
so
[tex](\frac{6}{6})\frac{2}{7}=\frac{12}{42}[/tex]
therefore
[tex]x=\£12\\y=\£42[/tex]
Part 3) For 8 metres of fabric
To find out the costs multiply the ratio by the fraction 8/8
so
[tex](\frac{8}{8})\frac{2}{7}=\frac{16}{56}[/tex]
therefore
[tex]x=\£16\\y=\£56[/tex]
Part 4) For 9 metres of fabric
To find out the costs multiply the ratio by the fraction 9/9
so
[tex](\frac{9}{9})\frac{2}{7}=\frac{18}{63}[/tex]
therefore
[tex]x=\£18\\y=\£63[/tex]
Solve the following systems: 3x+4y=0 2x+3y=1
Answer:
Answer is x= -4 and y= 3
Step-by-step explanation:
[tex]given \: equations \: are \\ 3x + 4y = 0 \: \: and \: 2x + 3y = 1 \\ multiply \: by \: 2 \: in \: first \: equation \\ 6x + 8y = 0 \\ multiply \: by \: 3 \: in \: second \: equation \\ 6x + 9y = 3 \\ subtracting \: the \: above \: mentioned \: equation \: \\ we \: get \: - y = - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ substitute \: y = 3 \: in \: first \: equation \\ 3x + 4(3) = 0 \\ 3x = - 12 \\ x = - 4[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
On a exam you get two points for each question answered correctly,zero points for each question left blank,and lose one point for each question answered incorrectly.what is your total score on the exam if you answer 22 questions correctly,leave 7 questions blank,and answer 5 questions incorrectly? P.S simplify expression
Answer:
Total score = 39 points
Step-by-step explanation:
For each correct question, you get 2 points, and there are 22 correct questions, so:
22 * 2 = 44 points.
For each question left blank, you get 0 points, and there are 7 questions left blank, so:
7 * 0 = 0 points
For each incorrect question, you get -1 point, and there are 5 incorrect questions, so:
5 * (-1) = -5 points.
The total number of points is:
Score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points
Which of the following triangle lengths form right triangles? Select all that apply
(7, 11, 13)
(10,24,26)
(12, 16, 20)
(12, 35, 37)
(13, 15, 19)
Answer:
B,C,D
Step-by-step explanation:
The correct option is (10,24,26) , (12, 16, 20) and (12, 35, 37).
What are the three sides of a right triangle?In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles.
What is considered a right triangle?A right triangle is a triangle with one right angle (one angle equal to 90°). The side opposite the right angle (the longest side) is called the hypotenuse. The remaining two sides (the sides that intersect to determine the right angle) are called the legs of the right triangle.
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