Question

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?

(1 point)
Responses

cos48°=x50
cosine 48 degrees is equal to x over 50

cos50°=50x
cosine 50 degrees is equal to 50 over x

cos48°=50x

Answer 1

To find the length of the cable that secures the tower to the ground, we can use trigonometry. The shadow of the tower (50 feet) and the height of the tower form a right triangle with the angle of elevation being 48°.

In this scenario, the cosine of the angle can help us relate the adjacent side (the length of the shadow) to the hypotenuse (the length of the cable). The correct setup using cosine should be:

\[ \cos(48°) = \frac{50 , \text{(the length of the shadow)}}{x , \text{(the length of the cable)}} \]

Rearranging this gives:

\[ x = \frac{50}{\cos(48°)} \]

Given the options provided, the appropriate response format would be:

cos48° = 50/x

This correctly sets up the relationship needed to find the length of the cable, where \(x\) is the length of the cable securing the tower.

So, the correct choice is: cos48° = 50/x