Huang is standing 14 meters from the base of a kite. The kite string makes a 67°

Question

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=69.05 m
𝑥
=
69.05

𝑚
x=69.05 m
𝑥
=
69.05

𝑚

x=15.21 m

Answer 1

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

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

In this case:

• The adjacent side is the distance from Huang to the base of the kite (14 m).
• The hypotenuse is the length of the kite string (x).
• \(\theta\) is 67°.

Rearranging the formula gives us:

\[ x = \frac{14}{\cos(67°)} \]

Calculating this step-by-step, we first find \(\cos(67°)\):

\[ \cos(67°) \approx 0.3907 \]

Now, we can substitute this value into the equation:

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

Thus, the length of the kite string (x) rounded to the nearest hundredth is:

\[ x \approx 35.83 , \text{m} \]

So the correct answer is:

x = 35.83 m