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]
