A wooden plank is leaning against an outside wall of a building. The bottom of the plank is 3 ft from the wall. Find each of the following values, and show all your work.

(A) Find the approximate length of the plank. Round to the nearest tenth of a foot.

Given that the distance of the ground is 3ft.

In order to get the length of the plank,

we can use the this one.

cos 49 = ground / plank

cos 49 = 3 / plank

plank = cos 49 / 3

plank = 0.10 ft

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

The remaining angle is equal to

angle = 180 - (90+49)

angle = 41

Finding the height.

tan 41 = height / ground

tan 41 = height / 3

height = tan 41 / 3

height = 0.05 ft.

(A) 0.10 feet

(B) 0.05 feet