Math CentralQuandaries & Queries


Question from Rafael, a student:

A vertical radio tower is located on the top of a hill that has an angle of elevation of 10 degrees. A 70-foot guy wire is attached to the tower 45 feet above the hill.

a. Make a drawing to illustrate the situation
b. What angle does the guy wire make with the side of the hill?
c. How far from the base of the tower is the guy wire anchored to the hill?

What confuses me about this problem is the visual situation. Isn't the angle of the guy wire with the side of the hill the same as the angle of elevation? And if not, then how is one supposed to find the other angles without any more information?


I think this is the situation being described.

hilll and tower

T is the point near the top of the tower where the guy wire is attached. The other end of the guy wire is at G. The length of TG is 70 feet and the length of BT is 45 feet. The tower is vertical so what is the measure of the angle TBG?

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