Question

A 37-foot ladder is leaning against a building. The angle between the ladder and the top of the building is 21. How far up the building does the ladder reach? Round to the nearest tenth.

Answer 1

34.5 feets

Explanation:

Length of ladder = 37 feet

Angle between ladder and top of building = 21°

Since ladder makes a right angle with the foot of the wall;

Angle the ladder makes with the ground :

(90° + 21° + θ) = 180°

111° + θ = 180°

θ = 180° - 111°

θ = 69°

To obtain the height, x of the building reached by the ladder ;

Using Pythagoras :

Sinθ = opposite / hypotenus

Sin 69° = x / 37

x = 37 * sin 69°

x = 37 * 0.9335804

x = 34.542475

x = 34.54 feets

Hence, the height up the building reached by the ladder is 34.5 feets