Question

A ladder leans against a 22-feet-tall apple tree. The base of the ladder forms a 42° angle with the ground. Approximately how tall must the ladder be to reach the top of the apple tree? A. 15 feet B. 16 feet C. 30 feet or D. 33 feet

Answer 1

(D) 33 feet

Explanation:

Given:

Height of the tree, h = 22 feet

angle, θ = 42°

Length of the ladder, l = ?

We know:

sin θ = Perpendicular / hypotenuse

So,

Sin θ = height of the tree / length of the ladder

$sin 42^0 = \frac{22}{l} \\\\0.67 = \frac{22}{l} \\\\l = 32.84 feet$

l = 32.84 feet ≈ 33 feet

Therefore, the length of the ladder be to reach the top of the apple tree is 33 feet.