A $200$ ft guy wire is attached to the top of a tower. If the wire makes a $55 ^ { \circ }$
Angle with the ground, how tall is the tower?
A) $163.8$ft
B) $90 \mathrm { ft }$
C) $265 \mathrm { ft }$
D) $85.4 \mathrm { ft }$
E) $255.6 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The height of the tower can be found using the sine function, since sine is opposite over hypotenuse in a right triangle. Here, the opposite side is the height of the tower (h), and the hypotenuse is the length of the guy wire (200 ft). So, $\sin(55^\circ) = \frac{h}{200}$. Solving for h gives $h = 200 \times \sin(55^\circ) \approx 163.8$ ft.

A 200200200 Ft Guy Wire Is Attached to the Top of a of a Tower

A $200$ Ft Guy Wire Is Attached to the Top of a of a Tower