Question

2. Another wooden plank is leaning against an outside wall of a building. The bottom of the plank is 9 ft from the wall. The length of the plank is 41 ft. Find each of the following values, and show all your work. (a) Find the value of x. Round to the nearest tenth of a degree. (b) Find the height above the ground where the plank touches the wall. Round to the nearest foot.

Answer 1

(A) Find the value of x. Round to the nearest tenth of a degree
Given that the distance of the ground is 9ft.
Length of the plank is 41 ft

In order to get the angle formed between the ground and the foot of the plank,

cos (theta) = ground / plank
cos (theta) = 9 / 41
cos (theta) = 0.21951...
theta = cos^-1(0.21951...)
theta = 77.3 degrees

(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.

Height = square root (plank^2 - ground^2)
Height = square root (41^2 - 8^2)
Height = square root (1600)
Height = 40

(A) 77.1 Degrees
(B) 40 feet