A 29 -ft ladder leans against a building so that the angle between the ground and the ladder is 83 ∘ . How high does the ladder reach on the building? Round to the hundredths. (2 decimal places)

Question

A 29-t ladder leans against a building so that the angle between the ground and the ladder is  83∘.

How high does the ladder reach on the building? Round to the hundredths. (2 decimal places) 

Answer 1

The building and the ground form a right angle, with the ladder the hypotenuse.

The angle given is between the ground and ladder, and sin is opposite/hypotenuse.

Thus, the height of the ladder is 29 sin(83°) = 28.7838383975983, which we round to 28.78

Answer 2

Draw and label a diagram!

h represents the height of the ladder.

h /. 29 = sin 83°

h = 29 sin 83°