Question

A new cell tower is being constructed and needs a guy-wire connected 157 feet up thetower and it needs to make an angle of 54° with the ground. What length does the wireneed to be?

Answer 1

Let's make a diagram of the problem:

The sine of an angle is given by the formula:

`\sin \theta=(opposite)/(hypotenuse)`

We know the opposite side measures 157 ft, and the angle is 54°. Replace these values, and solve for x (the hypotenuse):

`\begin{gathered} \sin 54=(157ft)/(x) \\ x=(157ft)/(\sin 54) \\ x=(157ft)/(0.809) \\ x=194.1ft \end{gathered}`

The wire needs to be 194.1 feet long