Question

a ladder leans against the sufe of a house. the angle of elevation of the ladder is 70 degrees when the bottom of the ladder is 12 ft from the side of the house. find the length of the ladder. round your answer to the nearest tenth.

Answer 1

≈ 35.1 ft

Explanation:

The model is a right triangle with ladder being the hypotenuse and the angle between the ground and the ladder is 70°

Using the cosine ratio, with l being the length of the ladder.

cos70° =
`(adjacent)/(hypotenuse)` =
`(12)/(l)` ( multiply both sides by l )

l × cos70° = 12 ( divide both sides by cos70° )

l =
`(12)/(cos70)` ≈ 35.1 ( to the nearest tenth )

The ladder is approx 35.1 ft long