Question

A 103-foot wire is used to support a utility tower. It runs from the tower to the ground and forms a 24° angle with the ground.

Answer 1

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Height of Tower = 41.8901 ft

Base to Ground Wire = 94.0905 ft

Step-by-step explanation:

So you want to find the opposing side of the angle, as well as the distance from the base to where the wire is attached to the ground. You would need to use CAH to find the ground, and SOH to find the height. To find the height or opposite, take the Sine of 24°, 0.4067, and times it by your hypoteneuse 103 to get an exact height of 41.8901 ft. Next, use the Cosine of 24°, 0.9135, and times that by your hypoteneuse 103 to get 94.0905 ft.

Here are the equations:

$sin(24)=\frac{h}{103}$

$cos(24)=\frac{h}{103}$