A200-foot long support wire attaches to a cell phone tower at a height of 50 feet from the ground.

to the nearest tenth of a foot, what is the distance along the ground from the center of the tower to the point where the wire touches the ground?

206.2 ft

21.2 ft

193.6 ft

7.1 ft

The answer is 193.6 ft. 

First draw a right triangle with the 50 feet tower as one of its legs and the other leg is represented by the distance from the tower to the wire. The 200 ft wire attached to the ground from the tower is the hypotenuse.

Using Pythagorean theorem, 

c^2 = a^2 + b^2

c = 200 ft
a = 50 ft
find b (distance from the tower to the attached wire)

200^2 = 50^2 + b^2

b = 193.6 ft

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