Question

Miguel lets out 123 ft. of kite string. The angle of elevation for the kite is 64°. What is the horizontal distance, x, from Miguel to the kite?(1 point) Responses x = 53.92 ft x = 53.92 ft x = 136.85 ft x = 136.85 ft x = 280.58 ft x = 280.58 ft x = 110.55 ft

Answer 1

To find the horizontal distance \( x \) from Miguel to the kite, we can use trigonometry, specifically the cosine of the angle of elevation.

In this case, we have:

- The length of the kite string (the hypotenuse) = 123 ft
- The angle of elevation = 64°

Using the cosine function:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Where:
- \(\theta = 64^\circ\)
- The adjacent side is the horizontal distance \( x \)
- The hypotenuse is 123 ft

Rearranging the equation to solve for \( x \):

\[
x = \text{hypotenuse} \cdot \cos(\theta) = 123 \cdot \cos(64^\circ)
\]

Calculating this, we first need to find the cosine of 64 degrees:

\[
\cos(64^\circ) \approx 0.4384
\]

Now, substituting this value back into the equation:

\[
x = 123 \cdot 0.4384 \approx 53.92 \text{ ft}
\]

Therefore, the horizontal distance \( x \) from Miguel to the kite is approximately **53.92 ft**.

So, the correct response is:

**x = 53.92 ft**