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. Item 5 Item 6 Item 7 Item 8 Item 9 x meters 67° 14 meters < Item 10 Item 11 Item 12 (1 point) Oz69.05 ft. 35.83 ft. Ox5.47 ft. 15.21 ft.

To solve for the length of the kite string (x) using the given information, we can use trigonometric functions. In this case, we can utilize the tangent function because we have the opposite side (14 meters) and we want to find the hypotenuse (the length of the kite string).

The relationship is given by:

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

Where:

• \( \theta = 67° \)
• \(\text{opposite} = 14\) meters (the height of the kite string from the point on the ground)
• \(\text{adjacent} = x\), the length of the kite string

However, we need to use the sine function because we want to find the hypotenuse (x):

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

We rearrange this to solve for the hypotenuse (the length of the kite string):

\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} = \frac{14}{\sin(67°)} \]

Now, we can calculate it:

1. Find \(\sin(67°)\):

   • Using a calculator, \(\sin(67°) \approx 0.9205\).

2. Calculate the length of the kite string (hypotenuse): \[ x = \frac{14}{0.9205} \approx 15.21 \text{ meters} \]

So, the length of the kite string is approximately 15.21 meters when rounded to the nearest hundredth.