Question

Huang is standing 14 meters from the base of a kite. The kite string makes a 67°
67
°
angle with the ground. Find x
𝑥
, the length of the kite string. Round to the nearest hundredth.(1 point)
Responses

x=35.83 m
𝑥
=
35.83

𝑚
x=35.83 m
𝑥
=
35.83

𝑚

x=5.47 m
𝑥
=
5.47

𝑚
x=5.47 m
𝑥
=
5.47

𝑚

x=15.21 m
𝑥
=
15.21

𝑚
x=15.21 m
𝑥
=
15.21

𝑚

x=69.05 m
𝑥
=
69.05

𝑚
x=69.05 m

Answer 1

To find the length of the kite string (x), we can use trigonometry. Given the distance from the base of the kite (14 meters) and the angle of elevation (67°), we can use the cosine function:

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

where:
- \(\theta = 67°\)
- adjacent side = 14 m (the distance from the base)
- hypotenuse = x (the length of the kite string)

Rearranging this formula to find \(x\):

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

Now, substituting the known values:

\[
x = \frac{14}{\cos(67°)}
\]

Calculating \(\cos(67°)\):

\[
\cos(67°) \approx 0.3907
\]

Now plug that into the equation:

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

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

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