Question

A cable is attached to a radio tower 100 ft

above the ground and forms an angle of 50 ( degrees ) with the ground. To the nearest foot, how long is the cable?

Answer 1

L = 131 feet

Explanation:

Right Triangles

The cable, the ground, and the radio tower form a right triangle with an angle of 90° located where the ground and the tower meet.

The cable is the hypotenuse of the triangle and the angle of 50° is opposite to the height of the radio tower.

To find the hypotenuse L we use the sine ratio:

`\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}`

`\displaystyle \sin 50^\circ=(100)/(L)`

Solving for L:

`\displaystyle L=(100)/(\sin 50^\circ)`

Calculating;

L = 131 feet