A Quick Guide to the 30-60-90 Degree Triangle
The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.
Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.
Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:
30, 60, and 90 degrees expressed in radians.
The figure illustrates the ratio of the sides for the 30-60-90-degree triangle.
A 30-60-90-degree right triangle.
A 30-60-90-degree right triangle.
If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:
Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.
Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.
Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.
Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.
Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.
In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?
Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:
The long side of a 30-60-90-degree triangle.
A scenic overlook which extends over a ravine is shaped like a kite.
Find M
A) 105°
B) 102°
C) 51°
D) 204°
Answer:
b
Step-by-step explanation:
i did jajajajajajaja jajajajjaja
the measure of angle X is [tex]\( 104^\circ \).[/tex]
To calculate the measure of angle X in a kite-shaped scenic overlook, we'll follow these steps:
Write the equation representing the sum of the measures of all the angles in the kite, which is [tex]\( 360^\circ \).[/tex]
Identify the two angles that are equal in the kite, which are angles X and Z.
Write the equation representing the sum of these angles and the given angle measures.
Solve for the measure of angle X.
Now, let's perform the calculation:
Equation representing the sum of the measures of all the angles in the kite:
[tex]\[ \angle X + \angle Y + \angle Z + \angle W = 360^\circ \][/tex]
Identify the two equal angles:
Since the kite has two pairs of adjacent sides that are equal, the angles opposite these sides will be equal. So, [tex]\( \angle X = \angle Z \).[/tex]
Write the equation representing the sum of these angles and the given angle measures:
[tex]\[ \angle X + 40^\circ + \angle X + 112^\circ = 360^\circ \][/tex]
Solve for the measure of angle X:
[tex]\[ 2\angle X + 152^\circ = 360^\circ \] \[ 2\angle X = 360^\circ - 152^\circ \] \[ 2\angle X = 208^\circ \] \[ \angle X = \frac{208^\circ}{2} \] \[ \angle X = 104^\circ \][/tex]
So, the measure of angle X is [tex]\( 104^\circ \).[/tex]
The complete question is:
A scenic overlook which extends over a ravine is shaped like a kite.
Find mZX
A) 105°
B) 102°
C) 51°
D) 204°
Identify the x- and y-intercepts of the graph
Answer:
see explanation
Step-by-step explanation:
The x- intercept is where the graph crosses the x- axis, that is
( [tex]\frac{1}{3}[/tex], 0 )
The y- intercept is where the graph crosses the y- axis, that is
(0, 1 )
A polygon with 4 sides is shown with its exterior angles. The exterior angles are 140 degrees, 34 degrees, 56 degrees, and x degrees. What is the value of x?
Given:
Given that the polygon has 4 sides with its exterior angles.
The exterior angles are 140°, 34°, 56° and x°
We need to determine the value of x.
Value of x:
We know that, the exterior angles of a polygon add up to 360°
Thus, we have;
[tex]140^{\circ}+34^{\circ}+56^{\circ}+x=360^{\circ}[/tex]
Adding the terms, we have;
[tex]230^{\circ}+x=360^{\circ}[/tex]
Subtracting both sides of the equation by 230, we get;
[tex]x=130^{\circ}[/tex]
Thus, the value of x is 130°
Final answer:
The value of the unknown exterior angle x in the quadrilateral is 130 degrees, calculated by subtracting the sum of the given exterior angles from the total sum of 360 degrees.
Explanation:
The student is asking about finding the value of an unknown exterior angle (x) in a quadrilateral. In geometry, the sum of the exterior angles of any polygon always equals 360 degrees. Given that three of the exterior angles are provided as 140 degrees, 34 degrees, and 56 degrees, we can find the value of the unknown exterior angle x degrees by subtracting the sum of these provided angles from 360 degrees.
First, we add the given angles:
140 degrees + 34 degrees + 56 degrees = 230 degrees
Next, we subtract the total from 360 degrees to get the value of x:
360 degrees - 230 degrees = 130 degrees
Therefore, the value of x, the unknown exterior angle of the quadrilateral, is 130 degrees.
How long does it take a runner to run 12km if he is running at a speed of 7km/h
Answer:
about an hour and 42 minutes
Step-by-step explanation:
Time=Distance/Speed
Answer:
1.714285714285714 hours
Step-by-step explanation:
12/7
A rectangle has a length of x + 9 and a width of x - 1. Which equation below
describes the perimeter, P, of the rectangle in terms of x? *
A: P=4x+16
B: P=2x+8
C: P=x+8
D: P=x^2+8x-9
Answer:
A
Step-by-step explanation:
P = 2 (W+L)
P = 2 (x+9+x-1)
P = 2 (2x+8)
P = 4x+16
The equation P = 4x+16 describes the perimeter, P, of the rectangle in terms of x. The correct answer would be option (A).
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
A rectangle has a length of x + 9 and a width of x - 1.
P = 2 (L + W) ....(i)
Substitute the values of L = x + 9 and W = x-1 in the above equation,
P = 2 (x+9+x-1)
P = 2 (2x+8)
P = 4x+16
Thus, the equation P = 4x+16 describes the perimeter.
Hence, the correct answer would be an option (A).
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Which expression is equivalent to 81 Superscript one-third?
Answer:
A. on edge
Step-by-step explanation:
Answer:
A) 3[tex]\sqrt[3]{3}[/tex]
Step-by-step explanation:
Hope this help, I got it right on Edge.
What is the Vertex? y = 3x ^2 + 12x − 10
Answer: -2,-22
Step-by-step explanation:
Which of the following constructions show the construction of an incircle
Answer:
the answer is B
what two fractions are between 6/9 and 7/9
i would be so greatful if someone can help me with this
Which number is a rational number? √25 √32 √50 √63
Answer:
√25
Step-by-step explanation:
√25 is a perfect square and simplifies to 5.
A rational number is any number that can be expressed as a quotient or fraction of two integers, with the denominator not equal to zero. Among the options, √25 is the only rational number as it equals to 5 which can be expressed as a fraction (5/1). The others are not rational as their square roots are not exact whole numbers.
Explanation:The question is asking which number among the given options is a rational number. Rational numbers can be any number that can be expressed as a quotient or fraction p/q of two integers, with the denominator q not equal to zero. In this case, we need to find out which of the square root numbers is rational.
The square of √25 is 25, so √25 equals to 5 which is surely a rational number, because it can be expressed as a fraction 5/1. So, the rational number from the given options is √25.
The square roots of the other numbers are not exact whole numbers and therefore aren't rational numbers. For example, √32, √50, and √63 are approximately 5.66, 7.07, and 7.94 respectively, and these cannot be expressed as exact fractions.
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Select statistical or not statistical do you classify each question.
Answer:
statistical, not statistical, not statistical
Step-by-step explanation:
Answer:
1. statical, 2. not statical, 3. not statical
Step-by-step explanation:
Which equation can be used to find the volume of this solid? A rectangular prism with a length of 5 centimeters, width of 4 centimeters, and height of 2 centimeters.
HHHHHHHHHHHHHEEEEEEEEEEEELLLLLLLLLLLLPPPPPPPPPPP MMMMMMMMMEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I think its A
Step-by-step explanation:
Answered a question like that in my test
Answer:
A) V=2x4x5
Step-by-step explanation:
because im a helping hand
What type of number can be written as a fraction p/q, where p and q are
integers and qis not equal to zero?
Answer:
Rational Numbers.
Step-by-step explanation:
These include terminating and repeating decimals. Numbers that can't be expressed as the type of fraction you've described are called Irrational Numbers.
help plz
6yd - 2ft 7in
Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two
integers?
-23
-5
9
14
Answer:
23
Step-by-step explanation:
here
9 and 14. are numbers
sum is 9 +14 = 23
what is the value of x?
(geometry question)
Given:
The interior angles of the triangle are 44°, 3t - 45° and x - 15°
The exterior angle of the triangle is 4t - 29°
We need to determine the value of x.
Value of t:
The value of t can be determined using the exterior angle theorem.
Applying the theorem, we have;
[tex]44+3t - 45=4t-29[/tex]
[tex]3t - 1=4t-29[/tex]
[tex]-t - 1=-29[/tex]
[tex]-t=-28[/tex]
[tex]t=28[/tex]
Thus, the value of t is 28.
Value of x:
The exterior angle 4t -29 and the interior angle x - 15 are linear pairs.
Since, linear pairs add up to 180°, we have;
[tex]4t-29+x-15=180[/tex]
Substituting t = 28, we get;
[tex]4(28)-29+x-15=180[/tex]
[tex]112-29+x-15=180[/tex]
[tex]x+68=180[/tex]
[tex]x=112[/tex]
Thus, the value of x is 112.
Nick cleans his room in 1 10 in a hour room for 3 minutes
This word problem doesn't make sense. Rephrase then I can solve. I believe you need units for the 110. I do not know what the 110 is.
A number K increased by 10 is the same as 24 what’s the equation
Final answer:
The equation for finding the value of K when increased by 10 equals 24 is K + 10 = 24, and solving it results in K = 14.
Explanation:
A number K increased by 10" is represented by K+10.
"Is the same as" means equal to.
"24" is represented by 24.
Therefore, we can express this relationship as an equation where the left side represents "a number K increased by 10" and the right side represents "24."
The equation to represent the situation where a number K increased by 10 equals 24 is:
K + 10 = 24
This equation signifies that when the unknown number K is augmented by 10, the resultant value equals 24. It serves as a concise representation of the given condition, enabling the determination of K by solving the equation.
Through such algebraic manipulation, one can discern that the value of K:
K = 24 - 10 = 14
2x+8y=4. x=−3y+5. substitution method
Your answer is Y= -3.
Answer:
(x, y) = (14, -3)
Step-by-step explanation:
You are given an expression for x, so it is convenient to use that to substitute for x.
2(-3y +5) +8y = 4
-6y +10 +8y = 4 . . . . . eliminate parentheses
2y = -6 . . . . . . . . . . . . subtract 10, collect terms
y = -3 . . . . . . . . . . . . . divide by 2
x = (-3)(-3) +5 = 14 . . . use the second equation to find x
The solution is (x, y) = (14, -3).
What is the probability that a person older than 35 has a hemoglobin level less
Answer:
has a hemoglobin level between 9 and 11 is 0.284.
Step-by-step explanation:
Help me find my answer please
Answer:
f = - [tex]\frac{19}{7}[/tex]
Step-by-step explanation:
Given f varies directly with m then the equation relating them is
f = km ← k is the constant of variation
To find k use the condition that f = - 19 when m = 14, thus
- 19 = 14k ( divide both sides by 14 )
- [tex]\frac{19}{14}[/tex] = k
f = - [tex]\frac{19}{14}[/tex] m ← equation of variation
When m = 2, then
f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]
Variable expression:
Four times the result of 3 times a number subtracted from 2.
Answer:
8-12n
Step-by-step explanation:
We can name "a number," "n."
4(2-3n)
Distribute.
4*2=8
4*-3n=-12n
8-12n
How many degrees are in the period of y = cos (3x)
Answer:
Step-by-step explanation:
cos(3x)=cos (3x+2π)=cos (3x+360)
period for 3x=360°
period=360/3=120°
Final answer:
The period of the function y = cos(3x) is π/3 or 120 degrees, since the coefficient '3' in the function's argument compresses the usual period of cos(x) by a factor of three.
Explanation:
The period of a trigonometric function represents the length of one complete cycle of the function. For the function y = cos(3x), we are dealing with a cosine function that has been horizontally compressed by a factor of 3. The standard period of the cosine function is 2π radians. However, the presence of the 3 within the argument of the cosine function means that the period is reduced by a factor of 3, because the function completes its cycle 3 times faster than the standard cosine function.
To find the period of the given function, we divide the standard period of the cosine function by the coefficient of the x variable inside the function:
Standard period of cos(x) = 2πPeriod of cos(3x) = ÷ 3Calculated period = 2π / 3Therefore, the period of y = cos(3x) is π/3 or approximately 120 degrees.
Please help if you can
Thank you!!
Answer:
0.67
Step-by-step explanation:
2/6 is shaded red, and 4/6 is shaded white. 4/6 is simplified to 2/3, 2/3 as a decimal is 0.67.
The table shows the length of hospital stay for 21 randomly selected adult patients. What is the interquartile range of this data?
To calculate it, first order your data points from least to greatest, then determine your first and third quartile positions by using the formulas (N+1)/4 and 3*(N+1)/4 respectively, where N is the number of points in the data set.
after you do that then say IQ=Q3-Q1
Answer:
8.5
Step-by-step explanation:
To calculate it, first order your data points from least to greatest, then determine your first and third quartile positions by using the formulas (N+1)/4 and 3*(N+1)/4 respectively, where N is the number of points in the data set.
after you do that then say IQ=Q3-Q1
What does πr2 in the example represent in the cylinder and the cone?
Answer:
Thats and area of a circular cylinder
Step-by-step explanation:
yeah thats all
Which phrases can be used to represent the inequality 12 minus 3 x greater-than-or-equal-to 9? Select two options.
Twelve less than three times a number is greater than or equal to nine.
Twelve less than three times a number is at least nine.
Twelve less three times a number is at least nine.
Twelve minus the product of three and a number is no more than nine.
Twelve minus the product of three and a number is no smaller than nine.
The phrases that represent the inequality 12 minus 3x greater-than-or-equal-to 9 are 'Twelve less than three times a number is greater than or equal to nine' and 'Twelve minus the product of three and a number is no smaller than nine.'
Explanation:The phrases that can be used to represent the inequality 12 minus 3x greater-than-or-equal-to 9 are:
Twelve less than three times a number is greater than or equal to nine. In this phrase, a number can be any variable or value that satisfies the given inequality.Twelve minus the product of three and a number is no smaller than nine. This phrase represents the same inequality using different wording.Learn more about Inequality here:https://brainly.com/question/40505701
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The phrases 'Twelve less than three times a number is greater than or equal to nine' and 'Twelve less than three times a number is at least nine' correctly represent the inequality 12 minus 3x greater-than-or-equal-to 9.
Explanation:The inequality 12 minus 3x greater-than-or-equal-to 9 can be represented in two ways among the given phrases. The correct phrases are 'Twelve less than three times a number is greater than or equal to nine' and 'Twelve less than three times a number is at least nine'. In both phrases, 'three times a number' represents '3x', 'twelve less than' represents '12 minus', and 'greater than or equal to nine' or 'at least nine' represents 'greater-than-or-equal-to 9'.
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The radius of a circle is 3 m. Find its area to the nearest tenth
Answer:
28.26
Step-by-step explanation:
3^2*3.14 = 28.26
To find area you square the radius and then multiply by 3.14 or π pi
Rounded to the nearest tenth, the area of the circle is approximately 28.3 square meters.
To find the area of a circle, we can use the formula:
Area = π (radius)²
Given that the radius is 3 meters, we substitute this value into the formula:
Area = π(3²)
Area = 9π
Since we are asked to round the area to the nearest tenth, we can approximate the value of π as 3.14:
Area ≈ 3.14 x 9
Area ≈ 28.26
Rounded to the nearest tenth, the area of the circle is approximately 28.3 square meters.
The area of a circle is calculated by multiplying the square of its radius by the mathematical constant π (pi). In this case, with a radius of 3 meters, the area is approximately 28.3 square meters. Rounding the decimal to the nearest tenth gives us the final result of 28.3 square meters.
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I need help guys I don’t understand this
Answer:
3:2 Three boxes next to two boxes.
Step-by-step explanation:
A ratio is like comparing things to others. Like if I had 3 cookies and you had 2 cookies the ratio would be 3:2. Three boxes next to two boxes.