Question

Huang is standing 14 meters from the base of a kite. The kite string makes a 67° angle with the ground. Find x, the length of the kite string. Round to the nearest hundredth.(1 point)Responsesx=15.21 mx equals 15.21 mx=5.47 mx equals 5.47 mx=69.05 mx equals 69.05 mx=35.83 m

Answer 1

To find the length of the kite string (\( x \)), we can use the sine function since we have the angle and the adjacent side (the distance from Huang to the base of the kite).

In this case:
- The angle \( \theta \) is 67°.
- The adjacent side (distance from the base) is 14 meters.

Using the cosine function:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
we can rearrange it to find \( x \):
\[
\text{hypotenuse} = \frac{\text{adjacent}}{\cos(\theta)}
\]
Substituting the known values:
\[
x = \frac{14}{\cos(67°)}
\]

Now calculate \( \cos(67°) \):
\[
\cos(67°) \approx 0.3907
\]
So,
\[
x \approx \frac{14}{0.3907} \approx 35.83 \, \text{m}
\]

Rounding to the nearest hundredth:
\[
x \approx 35.83 \, \text{m}
\]

Therefore, the length of the kite string is approximately \( x = 35.83 \, m \).