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:
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \sin 50^\circ=\frac{100}{L}[/tex]
Solving for L:
[tex]\displaystyle L=\frac{100}{\sin 50^\circ}[/tex]
Calculating;
L = 131 feet
