Chapter 9.1, Problem 43E

To determine

To find: The approximate height of the building.

Answer to Problem 43E

The approximate height of the building is $\text{427}$ meters.

Explanation of Solution

Given information:

Line 1: Eye level is $1.5$ meters.

Line 2: Standing $75$ meters from the base.

Line 3: Estimated angle is ${80}^o$ .

Calculation:

The height of the building is $h$ meters, the person is at $75$ meters away from the foot of the building.

The angle of the elevation to the top of the building is ${80}^o$ .

The objective is to find the height of the building.

The visual representation of the data is :

  

Write an equation and solve to get the height $h$ .

  $\begin{array}{c}\tan {80}^0=\frac{\text{Opposite side}}{\text{Adjacent side}}\\ =\frac{h}{75}\end{array}$

Multiply both side by 75.

  $\begin{array}{c}75\tan {80}^0=h\\ h=75*5.6713\\ =425.3475\end{array}$

Total height of the building is eyesight $+h=1.5+425.35=426.85m.$

Therefore, the approximate height of the building is $427$ meters.