Question

Aladder leans against the side of a house. The angle of elevation of the ladder is 63% and the top of the ladder is 15 ft from the ground. Find the length of theladder. Round your answer to the nearest tenth

Answer 1

According to the diagram and the information given, to find the length of the ladder we can use trigonometric ratios. More specifically, we need to use sine, which is the ratio between the opposite leg to a given angle and the hypotenuse.

In this case, the given angle is 63° and the opposite leg to it is 15. Use these values to find the hypotenuse of the triangle formed, which is the length of the ladder.

`\begin{gathered} \sin 63=(15)/(h) \\ h=(15)/(\sin 63) \\ h=(15)/(0.89) \\ h=16.8 \end{gathered}`

The length of the ladder is 16.8 ft