Question

20-ft ladder is leaning against a building. if the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? how high does the ladder reach on the building?

Answer 1

72.5⁰

19.1 ft

Explanation:

Picture a right triangle with hypotenuse of 20 ft (length of the ladder), short leg of 6 ft and the missing leg (x) as the height the ladder reaches on the building. Use the Pythagorean theorem to find the missing leg first, then the angle:

20² = 6² + x²

x² = 20² - 6² = 400 - 36 = 364

x = √364 = 19.1 ft

angle ∅ of elevation of the ladder :

sin∅ = 19.1/20

∅ = sin⁻1(19.1/20) = 72.5⁰