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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.

Sagot :

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:

[tex]\sin (32)=\frac{AC}{AB}[/tex]

this is equivalent to:

[tex]\sin (32)=\frac{166}{AB}[/tex]

solving for AB, we get:

[tex]AB\text{ = }\frac{166}{\sin(32)}\text{ = 313.}25\approx313.3[/tex]

thus the correct answer is:

[tex]AB\text{ =}313.3[/tex]

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