Answers
Using the law of sins that is given, you can write the following proportion.
3/sin(40) = c/sin(45)
All you have to do to solve for C is to multiply by sin(45). In the proportion, the letter are the side lengths and the trig ratios are of the angle opposite the side.
[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]
EXPLANATION
The sum of the interior angles of the given triangle is
[tex]180 \degree[/tex]
This implies that
[tex]A + 95 \degree + 45 \degree = 180 \degree[/tex]
We group like terms to get,
[tex]A = 180 - 140[/tex]
[tex]A = 40 \degree[/tex]
The law of sines is given by,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c} [/tex]
Based on our known values, we use,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(C) }{c} [/tex]
We now substitute the values to get,
[tex] \frac{ \sin(40 \degree) }{3} = \frac{ \sin(45 \degree) }{c} [/tex]
We reciprocate both sides of the equation to get,
[tex] \frac{ 3}{\sin(40 \degree)} = \frac{ c }{\sin(45 \degree)} [/tex]
We now multiply both sides by
[tex] \sin(45 \degree) [/tex]
to get,
[tex] \frac{3 \sin(45 \degree)}{\sin(40 \degree)} =c[/tex]
or
[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]
The correct answer is B.
Related Questions
Work the answer out n I’ll give xtra points
Answers
_____
The sheet of 100 is 9+1 = 3 groups of 3 sticks with 1 left over.
The 2 sticks with the one left over are 3 groups of 1.
The 6 singles are 3 groups of 2.
Altogether, you have 3 groups of (3 sticks +1 stick +2 singles).
from the top of a lighthouse 210 feet high, the angle created by the line of sight to a boat is 27°. find the distance of the boat to the light house.
Answers
This is a trigonometry problem. You must draw a triangle with the lighthouse and the boat. You are given the lighthouse height and the angle to the boat.
Using this information, you can set up a tangent ratio:
tan(27) = x/210
Solving this will give you:
0.5095 = x/210
107 = x
Convert fraction with numerator 7 and denominator 8 to a decimal.
0.375
0.875
0.925
0.965
Answers
Answer:
BStep-by-step explanation:
The measure of three angles of a triangle are (2x)°, (3x)° and (x + 60)°. What is the value of x?
Answers
6x+60=180
6x=120
x=20
Aubrey is painting a mural of an ocean scene. The triangular sail on a sailboat has a base of 4 feet and a height of 6 feet. Aubrey will paint the sail using a special white paint. A can of this paint covers 10 square feet. How many cans of white paint will Aubrey need?
Answers
(2)x6
12/10
1.2
2 Cans because you cant buy .2 of a can
Final answer:
Aubrey requires 2 cans of white paint to cover the triangular sail with an area of 12 square feet, given that one can covers 10 square feet.
Explanation:
Aubrey is painting a triangular sail as part of a mural with a base of 4 feet and a height of 6 feet. To calculate the area of the triangle, the formula is 1/2 × base × height. Thus, the area is 1/2 × 4 × 6, which equals 12 square feet. One can of special white paint covers 10 square feet. Therefore, Aubrey will need to use 2 cans of paint to cover the entire sail, since you can't purchase a fraction of a can.
Which statement is true?
All rectangles are parallelograms.
All rectangles are squares.
Some triangles are quadrilaterals.
Every rhombus is a square.
Answers
Answer:
A
Step-by-step explanation:
All rectangles are parallelograms and all their sides are parallel.
The diagram shows the dimensions of the pool cover for a gotel pool.The numbers are 10ft 20ft 45 ft 8 ft 8 ft 8ft What is the area of the pool cover
Answers
Answer:
684
Step-by-step explanation:
see photo for step by step explanation.
The area of the pool is the amount of space on it.
The area of the pool is 684 square feet
The dimensions of the pool are:
10ft by 20ft, 8ft by 20ft and 27ft by 12ft
The area of the pool is then calculated as:
A = 10 * 20 + 8 * 20 + 27 * 12
Evaluate the products
A = 200 + 160 + 324
Evaluate the sums
A = 684
Hence, the area of the pool is 684 square feet
Read more about areas at:
https://brainly.com/question/24487155
Which line segment is a radius of circle F?
ED¯¯¯¯¯
AC¯¯¯¯¯
DC¯¯¯¯¯
FE¯¯¯¯¯
Answers
Write the ordered pairs that represent the location of Sam and the theater
Answers
The question seems to require using ordered pairs to locate Sam and the theater, but lacks the specific coordinates or context needed for a precise answer. Ordered pairs are essential in geometry for representing positions.
Explanation:The question seems to pertain to locating positions or objects using ordered pairs, which falls under the domain of algebra and geometry in mathematics. An ordered pair (x, y) is used to define the positions on a plane, with 'x' representing the horizontal component and 'y' representing the vertical component.
Unfortunately, the question lacks specific information about the coordinates of Sam and the theater, making it impossible to provide exact ordered pairs without additional context. In scenarios involving maps or spatial planning such as finding locations in a city or arranging objects with a spatial relation to each other, ordered pairs serve as a crucial means of representation.
Exercises involving ordered pairs deepen understanding of coordinate systems, which are fundamental in geometry and crucial for various applications in science and engineering.
A tree 63 ft high casts a 38 ft shadow. How tall is a tree that casts a 52 ft shadow at the same time of the day? (to the nearest tenth
Answers
1.368 x 63 = 86.21
tree is 86.2 feet high
Lisa built a rectangular flower garden that is 4 feet wide and has a perimeter of 26 feet. what is the length of Lisa's flower garden?
Answers
9+9+4+4=26
4+4=8
26-8=18
18 divided by 2= 9
Which of the fraction below is equivalent to 1/3? Show why that fraction is equivalent to 1/3. 4/5, 4/6, 4/9, 4/12
Answers
To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. The fraction that is equivalent to 1/3 is 4/12.
Explanation:To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. Let's go through each option:
4/5: This fraction is not equivalent to 1/3 because 4/5 is greater than 1/3.4/6: To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2.4/6 simplifies to 2/3, which is not equivalent to 1/3.4/9: This fraction is not equivalent to 1/3 because 4/9 is greater than 1/3.4/12: To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4.
4/12 simplifies to 1/3, which is equivalent to 1/3.
Therefore, the fraction that is equivalent to 1/3 is 4/12.
Joey has 8 pairs of socks in his drawer 5 of them are white. what percent of colored socks does Joey have
Answers
We usually don’t count white socks as colored, so keep that in mind for the problem.
There are 5 pairs of white socks.
8-5=3
There are 3 pairs of colored socks.
3/8= fraction of colored over the whole amount.
Make 3/8 into a decimal. (Divide 3 by 8)
3/8= .375
Now, we just have to make that into a percentage.
.375= 37.5%
37.5% of the socks were colored.
I hope this helps!
~kaikers
Since 5 out of 8 pairs of socks are white, 3 pairs of socks are colored.
3/8 = 0.375 = 37.5% of the socks are colored
Maria says her pencil is 1.7 meters long is this measurement reasonable
Answers
10 POINTS AND BRAINLIEST
Which set of numbers is finite?
Even numbers between 1 and 89
Real numbers greater than 1
Rational numbers between 1 and 2
Whole numbers with tens digits at zero
Answers
Answer: #1
Please I need help with questions 2-4 and it’s very hard and I’m struggling with it and if you need to see the picture big then click on it and it will be big
Answers
.. = 12.35976*10⁸
.. ≈ 1.236*10⁹ . . . . . people living in India
3) The mantissa was greater than 10, so a factor of 10 was removed from it and added to the exponent
4) (2.844*10⁹)/(4.5*10⁶) = (2.844/4.5)*10⁽⁹⁻⁶⁾ = 0.632*10³
Amy apparently adjusted the magnitude of the mantissa without adjusting the exponent. The correct normalized form is
.. 6.32*10²
sarah is training for a bike race. she rides her bike 5 3/4 miles in 1/3 hour. what is sarahs's rate in miles per hour?
Answers
Hope this helps!
Since it is 1/3 of an hour for 5 3/4 miles, multiply 5 3/4 x 3 . . .
5 3/4 = 23/4
3 = 3/1
23 x 3 = 69
4 x 1 = 4
Simplifying 69/4 . . .
69/4 = 17 1/4 <-----------
Sarah's rate is 17 1/4 miles per hour.
Hope this helps you.
Have a great day!
Mr shen likes for his homework assignment to have 2 addition problems for every 3 subtraction problems
Answers
Answer:
Options B, C and D are correct choices.
Step-by-step explanation:
Please consider the complete question.
Mr. Shen likes for his homework assignments to have 2 addition problems for every 3 subtraction problems.
Which of the following homework assignments could
Mr. Shen create?
Choose 3 answers:
A. 3 addition problems and 4 subtraction problems .
B. 6 addition problems and 9 subtraction problems .
C. 16 addition problems and 24 subtraction problems.
D. 8 addition problems and 12 subtraction problems.
E. 15 addition problems and 10 subtraction problems.
To solve our given problem, we need to find the number that have same ratio.
Let us compare each ratio.
A. [tex]\frac{3}{2}\neq \frac{4}{3}[/tex]
Since the ratio of corresponding numbers is not same, therefore, option A is incorrect.
B. [tex]\frac{6}{2}=\frac{9}{3}[/tex]
[tex]3=3[/tex]
Since the ratio of corresponding numbers is same, therefore, option B is the correct choice.
C. [tex]\frac{16}{2}=\frac{24}{3}[/tex]
[tex]8=8[/tex]
Since the ratio of corresponding numbers is same, therefore, option C is the correct choice.
D. [tex]\frac{8}{2}=\frac{12}{3}[/tex]
[tex]4=4[/tex]
Since the ratio of corresponding numbers is same, therefore, option D is the correct choice.
E. [tex]\frac{15}{2}\neq \frac{10}{3}[/tex]
Since the ratio of corresponding numbers is not same, therefore, option E is incorrect.
what is 5cm × 8cm × 10cm
Answers
Solve the equation and show all work please show steps!!
m/9 - 17=21
Answers
------------
Simplify
1/9m - 17 = 21
----------------
Add 17 to each side
1/9m-17+17=21+17
1/9m = 38
------------------------
Multiply each side by 9
9 * (1/9m) = 38 * 9
m = 342 is your answer
Solve the following equation: x^3+3x^2-10x=0
Answers
The GCM of those three terms is x. So group them by x.
x(x² + 3x - 10) = 0
factor x² + 3x - 10
x(x - 2)(x + 5) = 0
x = 0 , x = 2 , x = -5
Qual é o perímetro de um quadrado de 3,8 cm de lado ?E sua área?
Answers
Para encontrar el perímetro tienes que anadir 3.8, 4 veces o mulltiplicar por 4
3.8 + 3.8 + 3.8 + 3.8 = 15.2
3.8 x 4 = 15.2
15.2 es tu respuesta
Para encontrar el area multiplica 3.8 por 3.8
3.8 x 3.8 = 14.44
14.44 es tu area
Write to explain how to do bd an equivalent fracrion for the fraction 3/9
Answers
[tex] \dfrac{3}{9} = \dfrac{3 \div 3}{9 \div 3} = \dfrac{1}{3} [/tex]
[tex]\text {Answer = } \dfrac{1}{3} [/tex]
Answer:
1/3
Step-by-step explanation:
help meeeee plzzzzzzz
Answers
For a single roll of two dice, are rolling a sum of 6 and rolling doubles mutually exclusive events?
Answers
Answer: They are not mutually exclusive events.
Step-by-step explanation:
Let A be the event of getting a sum of 6 on dice.
Let B be the events of getting doubles .
A={ (1,5), (2,4), (3,3), (4,2), (5,1) }
B = { (1,1) , (2,2), (3,3), (4,4), (5,5), (6,6) }
Since we know that Mutaullty exclusive events are those when there is no common event between two events.
i.e. there is empty set of intersection.
But we can see that there is one element which is common i.e. (3,3).
So, n(A∩B) = 1 ≠ ∅
Hence, they are not mutually exclusive events.
Answer:
They are not mutually exclusive events.
Step-by-step explanation:
A square has side lengths of 7 inches. Find the length of the square’s diagonal.
Answers
7•7=49
7•7=49
49+49= 98
Now let’s find the square root of 98. I usually go to the hundredths place since I know 98 doesn’t have a perfect square.
9.9•9.9= 98.01 (the hundredths place rounded to that)
So the length of the square’s diagonal is about 9.9 inches.
Final answer:
The length of the square's diagonal with side lengths of 7 inches is found using the Pythagorean theorem, leading to a diagonal of approximately 9.899 inches.
Explanation:
To find the length of the square's diagonal when the side lengths are 7 inches, we can use the Pythagorean theorem. The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse. You can think of this as half of the square divided along the diagonal. Each of these triangles has two legs that are each equal to the side of the square and a hypotenuse which is the diagonal we want to find.
The formula for the Pythagorean theorem is a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse. Since the legs are both 7 inches (the side length of the square), we have:
7² + 7² = c²
49 + 49 = c²
98 = c²
This simplifies to:
c = √98
c ≈ 9.899 inches (rounded to three decimal places)
Therefore, the diagonal of the square is approximately 9.899 inches long.
a geometric sequence has an initial value of 25 and a common ratio of 1.8. Write a function to represent this sequence . Find.the 23rd term.
Answers
a_n = a_1•r^(n-1)
a_23 = 25•(1.8)^(23 - 1)
Can you finish?
23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].
Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]
What is geometric sequence?" Geometric sequence is defined as the sequence whose ratio of the consecutive terms is always constant."
Formula used
nth term of the geometric sequence
[tex]a_{n} = a r^{n-1}[/tex]
a = first term
r = common ratio
[tex]a_{n}[/tex] = nth term
According to the question,
First term of the geometric sequence 'a' = 25
Common ratio of the geometric sequence 'r' = 1.8
Substitute the value in the formula to get 23rd term,
[tex]a_{23} = 25(1.8)^{23-1}[/tex]
⇒[tex]a_{23} = 25(1.8)^{22}[/tex]
Function to represent this sequence
[tex]a, a(r),a(r)^{2} , a (r)^{3} , ....... ,a(r)^{n}[/tex]
= [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]
Hence, 23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].
Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]
Learn more about geometrical sequence here
https://brainly.com/question/11266123
#SPJ2
janet lit a 12-inch candle. she noticed that it was getting an inch shorter every 30 minutes in how many hours will the candle burn out support your answer with a reason
Answers
Guys please help me please...
Answers
To graph these equations, which are already in slope-intercept form:
For the freshmen, we begin with the y-intercept at (0, 100). Then for each unit of x (to the right), we raise the y-value by 50. So we can put another point at (1, 150), at (2, 200), at (3,250), and so on. Any one other point is sufficient to draw the line.
For the sophomore, we begin with the y-intercept at (0, 250), and increase y by 25 for each unit of x. So we can connect it with (1, 275), (2, 300), and so on.
If both lines are drawn, we will see the intersection point at (6, 400), which means that both groups have a cost of y = $400 at x = 6 rolls.
Write 30/80 as a percent
Answers
To workout this, divide the numerator by the denominator, sum this value to the integer part then multiply the result by 100%, so:
30/80 in percent = 30 ÷ 80 × 100% =
0.375 × 100% =
37.5%
3/8 = 0.375
0.375 = 37.5%
Hope this helped☺☺