Chapter 4, Problem 95RE

Solution

To find: the height of the building.

The height of the building is 470.5 m.

Given:

The angle of elevation of the top of a building from a point 100 m from the building on level ground is ${78}^{\circ }$ .

Concept used:

In a right triangle, tangent is the ratio of the opposite side to the adjacent side.

Calculation:

Let $h$ be the height of the building. Then the triangle is,

  

Now,

  $\begin{array}{c}\tan \left({78}^{\circ }\right)=\frac{h}{100}\\ \text{4}\text{.7046}=\frac{h}{100}\\ h=\text{470}\text{.463}\text{m}\\ h\approx 470.5\text{m}\end{array}$

Therefore the height of the building is 470.5 m.