Question

Tom 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 hundreth. (1 point)
Responses

69.05 m
69.05 m

35.83 m
35.83 m

15.21 m
15.21 m

5.47 m
5.47 m

Answer 1

To find the length of the kite string (x), we can use trigonometry. Given that Tom is standing 14 meters from the base of the kite and the kite string makes a 67° angle with the ground, we can use the cosine function.

The cosine of an angle in a right triangle relates the adjacent side (the distance from Tom to the base of the kite) to the hypotenuse (the length of the kite string):

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

Substituting the known values:

\[
\cos(67°) = \frac{14}{x}
\]

Now, to solve for \(x\):

1. Rearrange the equation:

\[
x = \frac{14}{\cos(67°)}
\]

2. Calculate \(\cos(67°)\):

\[
\cos(67°) \approx 0.3907
\]

3. Now substitute this value back into the equation:

\[
x = \frac{14}{0.3907} \approx 35.83
\]

So the length of the kite string, rounded to the nearest hundredth, is:

\[
\boxed{35.83 \text{ m}}
\]

Therefore, the correct response is **35.83 m**.