To find the length of the cable that secures the tower to the ground, we can consider the right triangle formed by the tower, the ground, and the cable.
- The tower represents the opposite side of the triangle.
- The shadow (50 feet) represents the adjacent side of the triangle.
- The cable, which is the hypotenuse of the triangle, connects the top of the tower to the ground where the tower is anchored.
Given that the angle is 48°, we can use the cosine function, which relates the adjacent side and the hypotenuse:
\[ \cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case, the adjacent side is 50 feet (the shadow), and we can label the length of the cable as \( x \).
Thus, the correct equation should be:
\[ \cos(48°) = \frac{50}{x} \]
To solve for \( x \), you can rearrange this:
\[ x = \frac{50}{\cos(48°)} \]
Now let's look at the options given:
- Option #1: cos48° = x/50
- Option #2: cos48° = 50/x
- Option #3: cos50° = 50/x
Option #2 is the correct setup:
\[ \cos(48°) = \frac{50}{x} \]
This means the answer is Option #2.
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