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Chapter 8: Q. 73 (page 519)

Chicago SkyscrapersThe angle of inclination from the base of the John Hancock Center to the top of the main structure of the Willis Tower is approximately 10.3掳. If the main structure of the Willis Tower is 1450 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.

Short Answer

Expert verified

The two skyscrapers are 7979 ft. apart.

Step by step solution

01

Step 1. Given information

The information given in the question is plotted in a diagram follows:

In this diagram we can see that there are two skyscrapers John Hancock center and the Willis Tower. We need to find the distance between the foots of the towers and given with the following information:

BC=1450ft.and鈭�CAB=10.3掳.

02

Step 2. Trigonometric equations involved

In鈭�ABCwehave,tan鈭�BAC=BCAB.

03

Step 3. Solving the equations to find the answer.

tan10.3掳=1450d,d=1450tan10.3掳,d=14500.1817鈮�7979ft.

So the distance between the foots of the towers is 7979 ft.

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