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Chapter 8: Q. 71 (page 518)

To measure the height of Lincoln鈥檚 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鈥檚 face is 32掳 and the angle of elevation to the top is 35掳, what is the height of Lincoln鈥檚 face?

Short Answer

Expert verified

The height of Lincoln鈥檚 face is 60.8 feet.

Step by step solution

01

Given Information

Given that to measure the height of Lincoln鈥檚 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鈥檚 face is 32掳 and the angle of elevation to the top is 35掳.

02

Solution

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

We have to find the height of Lincoln鈥檚 face.

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

So, in鈻�DBC,鈭�B=90掳,鈭�C=32掳

tan(32掳)=x800x=tan(32掳)脳800x=0.624脳800x=499.2feet

No, the height of the top.

In 鈻�ABC,鈭�B=90掳,鈭�C=35掳

tan(35掳)=y800y=tan(35掳)脳800y=0.700脳800y=560feet

Now the height of Lincoln鈥檚 face isy-x=560-499.2=60.8feet

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