Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 72° when the bottom of the ladder is 14 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

Answer 1

Length of ladder = 45.30 ft

Explanation:

Given data:

Distance between the bottom of the ladder and side of house = 14 ft

Angle of elevation of the ladder = 72°

To find length of the ladder.

From the data given to us we can construct a right triangle ABC.

For the Δ ABC

AC= 14 ft

∠A= 72°

We can apply trigonometric ratio to find side AB which is the length of the ladder.

`\cos72\°=(AC)/(AB)` [ ∵
`\cos\theta=(Adjacent\ side)/(Hypotenuse)` ]

Multiplying both sides by AB.

`AB\cos72\°=(AC)/(AB)* AB`

`AB\cos72\°=AC`

Dividing both sides by cos72°

`(AB\cos72\°)/(cos72\°)=(AC)/(cos72\°)`

`AB=(AC)/(cos72\°)`

Substituting value of AC and cos 72°

`AB=(14)/(0.309)`

`AB=45.30\ ft`

Thus, length of the ladder = 45.30 ft