Question

To measure the height of Lincoln’s caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are taken. If the angle of elevation to the bottom of Lincoln’s face is 32° and the angle of elevation to the top is 35°, what is the height of Lincoln’s face?

Short answer

The height of Lincoln’s face is 60.8 feet.

Step-by-step solution

Given Information

Given that to measure the height of Lincoln’s caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are taken. If the angle of elevation to the bottom of Lincoln’s face is 32° and the angle of elevation to the top is 35°.

Solution

We can draw a figure of the given problem as:-

We have to find the height of Lincoln’s face.

First, we will find the height of Lincoln’s face of the bottom.

So, in$△DBC,\angle B=90°,\angle C=32°$

$$\begin{gathered} \tan (32°)=\frac{x}{800} \\ x=\tan (32°)\times 800 \\ x=0.624\times 800 \\ x=499.2feet \end{gathered}$$

No, the height of the top.

In $△ABC,\angle B=90°,\angle C=35°$

$$\begin{gathered} \tan (35°)=\frac{y}{800} \\ y=\tan (35°)\times 800 \\ y=0.700\times 800 \\ y=560feet \end{gathered}$$

Now the height of Lincoln’s face is$y-x=560-499.2=60.8feet$