EXAMPLE 3.7.5

The diagram below shows Gomer's sailboat at anchor. At the time that he released the anchor, the sailboat was touching the channel marker buoy shown in the figure. After he has drifted 80 feet from the bouy he has let out 160 feet of anochor line. How deep is the water under the bouy?

A. 60 feet

B. 179 feet

C. 80 feet

D. 139 feet

SOLUTION

The depth of the water is the measure of one leg of a right triangle whose other leg measures 80 feet (the distance from the boat to the bouy) and whose hypotenuse measures 160 feet (the distance from the boat to the anchor, which is the same as the length of anchor line that has been let out). Let D be the depth. According to the Pythagorean Theorem:

160 squared equals D squared plus 80 squared
25,600 equals D squared plus 6,400
25,600 minus 6,400 equals D squared
19,200 equals D squared
The square root of 19,200 equals D.
D is about equal to 138.6.

The best choice is D.