Question

A ladder leans against the wall and reaches a point 24 ft up the wall. The base of the ladder is 6 feet from the wall.

a) To the nearest tenth, what angle does the the ladder make with the ground?
b) To the nearest tenth, how long is the ladder?

Answer 1

Hi

a.)75.96°

b.)24.74

Explanation:

This question is on angle of Elevation and Depression

a.)opposite=24,adjacent=6 so the Trigonometric function that connects them is Tan(a.k.a TOA)

TOA means Tanθ=opposite/adjacent

Tanθ=24/6

Tanθ=4

divide both sides by Tan

θ=Tan^-1 4

θ=75.96°

b.)looking for the hypotenuse

Let us use Pythagoras theorem

Hyp²=opp²+adj²

Hyp²=24² + 6²

Hyp²=576 + 36

Hyp²=612

Hyp=√612

Hyp=24.74