Question

A ladder leans up against a wall and makes a 60 degree angle with the ground. If it reaches 90 ft. up the wall, how long is the ladder? Round to the nearest tenth​

Answer 1

The length is approximately 103.92 ft

Explanation:

The angle the given ladder makes with the ground = 60°

The height to which the ladder reaches. h = 90 ft.

Assumption;

The angle formed between the wall and ground = 90°

The shape formed by the length, l, of the ladder the height to which the ladder reaches on the wall, h, and the ground, b, is a right triangle, with the length, l, of the ladder facing the 90° angle and the height, h, facing the 60° angle.

By sine rule, we have;

l/sin(90°) = h/sin(60°)

Therefore, the length l = sin(90°) × h/sin(60°) = 1 × 90/(sin(60°)) = 90/((√3)/2) = 2 × 90/√3 ≈ 103.92

The length, l ≈ 103.92 ft.