Question

A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 75 ∘ . How high does the ladder reach on the building?

Answer 1

The height of the building is 16.42 ft

Explanation:

Given;

length of the ladder, = 17 ft

angle between the ground and the ladder, θ = 75°

Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.

Apply the following trig-ratio to determine the height of the triangle;

`sin \theta = (opp)/(hypo)\\\\ sin (75^0) = (h)/(17)\\\\h = 17sin (75^0) \\\\h = 16.42 \ ft`

Therefore, the height of the building is 16.42 ft