Question

A radio transmission tower is 180 feet tall. How long should a guy wire be if it is attached 14 feet from the top and is to make an angle of 32° with the ground? Give your answer to the nearest tenth of a foot. Show your work.

Answer 1

Question:

A radio transmission tower is 180 feet tall. How long should a guy wire be if it is attached 14 feet from the top and is to make an angle of 32° with the ground?

Solution:

Consider the following diagram:

According to the above triangle, we get:

180-14 = 166

AC = 166 ft

applying the trigonometric identities to the triangle ACB, we get:

`\sin (32)=(AC)/(AB)`

this is equivalent to:

`\sin (32)=(166)/(AB)`

solving for AB, we get:

`AB\text{ = }(166)/(\sin(32))\text{ = 313.}25\approx313.3`

thus the correct answer is:

`AB\text{ =}313.3`