Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 61°, and the top of the ladder is 14 ftabove the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to thenearest tenth.

Answer 1

A ladder leans against the side of a house. The angle of elevation of the ladder is 61°, and the top of the ladder is 14 ft above the ground.

In the above diagram, AB is the ladder and AC is the house.

`\begin{gathered} \angle\text{ABC}=61^o \\ AC=14\text{ ft} \end{gathered}`

In th etriangle ABC,

`\begin{gathered} (AC)/(BC)=\tan 61 \\ (14)/(BC)=\tan 61 \\ BC=(14)/(\tan 61) \\ =7.76 \end{gathered}`

So, the distance from the bottom of the ladder to the side of the house is approximately 7.76 ft