Question

A board is leaning against a vertical wall, The board makes a 62 degree angle with the ground and touches the wall at a point that is 45 in, above the ground. What is the length of the board, rounded to the nearest inch?

Answer 1

Angle A = 62°
Angle B = 90°
Side a = 45
The length of the board is side b

Use the Law of Sines to find side b.
b / sin(B) = a / sin(A)
b / sin(90°) = 45 / sin(62°)
b = (sin(90°) x 45) / sin(62°)
b = 50.966

Rounded to the nearest inch is 51 inches.

Hope this helps!

Answer 2

Option C. 51 in.

Explanation:

In the given right angle triangle height is given as 45 in. above the ground.

Length of the board is making an angle of 62°with the ground.

Therefore by sine rule

sin 62° = height / hypotenuse

sin 62° = 45/h

0.8829 = 45/h

h = 45/0.8829 = 50.96 ≈ 51 in.

Therefore option C. 51 in. is the answer.