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: \\(\cos 48^{\circ}=\frac{x}{50}\\) option #2: \\(\cos 48^{\circ}=\frac{50}{x}\\) option #3: \\(\cos 50^{\circ}=\frac{50}{x}\\)

Explanation:

Step1: Identify triangle sides

We have a right triangle: the shadow (50 ft) is the adjacent side to the 48° angle, the cable length $x$ is the hypotenuse.

Step2: Apply cosine definition

Cosine of an angle = $\frac{\text{adjacent}}{\text{hypotenuse}}$. Substitute values:
$\cos 48^\circ = \frac{50}{x}$

Answer:

Option #2: $\cos 48^\circ = \frac{50}{x}$