Let's make a diagram of the problem:
The sine of an angle is given by the formula:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]
We know the opposite side measures 157 ft, and the angle is 54°. Replace these values, and solve for x (the hypotenuse):
[tex]\begin{gathered} \sin 54=\frac{157ft}{x} \\ x=\frac{157ft}{\sin 54} \\ x=\frac{157ft}{0.809} \\ x=194.1ft \end{gathered}[/tex]
The wire needs to be 194.1 feet long
