Question

A telephone tower casts a 50-foot shadow that makes a 48° angle with the ground. If Fiona wants to find the length of the cable that secures the tower to the ground, how should she set up the problem?

Option #1: cos48°=x50
cos
⁡
48
°
=
𝑥
50

Option #2: cos48°=50x
cos
⁡
48
°
=
50
𝑥

Option #3: cos50°=50x
cos
⁡
50
°
=
50
𝑥

(1 point)
Option # is the correct setup.

Answer 1

To find the length of the cable that secures the tower to the ground, we can use trigonometry. The angle given (48°) is between the ground and the line of the cable. The shadow (50 feet) represents the adjacent side of a right triangle, while the length of the cable (hypotenuse) is what we want to find.

Using the cosine function, which relates the angle to the adjacent side and hypotenuse, the setup is:

\[
\cos(48°) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{50}{x}
\]

Where:
- \( \cos(48°) \) is the cosine of the angle,
- 50 is the length of the shadow (adjacent),
- \( x \) is the length of the cable (hypotenuse).

Rearranging gives us:

\[
x = \frac{50}{\cos(48°)}
\]

Thus, the correct option is:

**Option #1: \( \cos 48° = \frac{x}{50} \)**