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

15.21 m
15.21 m

35.83 m
35.83 m

69.05 m
69.05 m

5.47 m

Answer 1

To solve for the length of the kite string \( x \), we can use trigonometric functions. The relationship between the angle, the opposite side (height of the kite), and the adjacent side (distance from Tom to the base of the kite) can be expressed using the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case, we do not have the height of the kite, but we can find the length of the kite string using the cosine function, since we know the angle and the distance from Tom:

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

Where:
- \(\theta = 67^\circ\)
- \(\text{adjacent} = 14 \text{ m}\) (distance from Tom to the base of the kite)
- \(\text{hypotenuse} = x\) (length of the kite string)

Rearranging the formula gives us:

\[
x = \frac{14}{\cos(67^\circ)}
\]

Now we need to calculate \(\cos(67^\circ)\):

Using a calculator:

\[
\cos(67^\circ) \approx 0.3907
\]

Then:

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

Thus, the length of the kite string \( x \) is approximately **35.83 meters**.

So, the correct answer is **35.83 m**.