Question

Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet awayfrom the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground.Paul and the house are both perpendicular to the ground. The angles between the top of thehouse, the mirror, and the ground and between Paul's eyes, the mirror and the ground arecongruent as shown in the image below:What is the height of the house? Show your work and explain your reasoning in completesentences (10 points)

Answer 1

using the trigonometric ratio

$\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{where,} \\ \text{opposite}=6ft \\ \text{adjacent=}5ft \\ \end{gathered}$$\begin{gathered} \tan \theta=\frac{6ft}{5ft} \\ \tan \theta=1.2 \end{gathered}$

To calculate the height of the house,

$\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{opposite}=h \\ \text{adjacent}=25ft \\ \tan \theta=1.2 \end{gathered}$

By susbstitution,

$\begin{gathered} 1.2=\frac{h}{25ft} \\ \text{cross multiply we will have} \\ h=1.2\times25ft \\ h=30ft \end{gathered}$

Therefore,

The height of the house= 30ft