Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 68°, and the top of the ladder is 13 ft above the ground. Find the distancefrom the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.

Answer 1

5.3ft

Step-by-step explanation

Given the following

Angle of elevation = 68degrees

height of the house (opposite) = 13ft

Required

Distance from the bottom of the ladder to the side of the house (adjacent) D

Using the SOH CAH TOA identity

tan theta = opposite/adjacent

tan 68 = 13/D

D = 13/tan68

D = 13/2.4751

D = 5.25

D = 5.3ft (to the nearest tenth)

Hence the distance from the bottom of the ladder to the side of the house is 5.3ft