Question

A cable is attached to a radio tower 100 ft

Answer 1

Answer:

L = 131 feet

Step-by-step 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:

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

$\displaystyle \sin 50^\circ=\frac{100}{L}$

Solving for L:

$\displaystyle L=\frac{100}{\sin 50^\circ}$

Calculating;

L = 131 feet