Answer to Question #154544 in Trigonometry for Hdhdhxgsbsb

Question

You were playing fetch with your dog and accidentally 

threw the toy and it got stuck on the roof of your 

house. You leaned the ladder against your house at a 

30° angle of elevation. The foot of the ladder is 7 feet 

from the foot of the house. How long is your ladder? 

Answer 1

Let $L=$ the length of the ladder, $\alpha=$ the angle of elevation, $H=$ the height of the house, and $X=$ the distance from the foot of the house to the foot of the ladder.

From the right triangle

$$\cos\alpha=\dfrac{X}{L}$$

Then

$$L=\dfrac{X}{\cos\alpha}$$

Given $\alpha=30\degree, X=7\ ft.$

Substitute

$$L=\dfrac{7}{\cos30\degree}=\dfrac{7}{\dfrac{\sqrt{3}}{2}}=\dfrac{14\sqrt{3}}{3}(ft)\approx8.083(ft)$$

The ladder is 8.1 foot long.