Chapter 12, Problem 7CT

To determine

Find the height of the building if the angle of elevation of a observer from the street to the top of a building is $55.6°$ and the observer is 150 feet away from the base of the building.

Answer to Problem 7CT

The height of the building is $219.1\text{ ft}$ .

Explanation of Solution

Given information: The angle of elevation of the observer is $55.6°$ and the person is 150 feet away from the bottom of the building.

Calculation: Consider that the height of the building is (BC) and the distance of the observer from the base of building is (AB) equal to 150 feet. Now by trigonometric ratio in triangle assumed below,

  

  $\begin{array}{c}\tan \left(55.6°\right)=\frac{BC}{AB}\\ \text{or, }BC=AB\tan \left(55.6°\right)\\ BC=\left(150\right)\tan \left(55.6°\right)\\ BC=219.1\text{ ft}\end{array}$

Hence the height of the building is $219.1\text{ ft}$ .