Kyra is standing 50 feet from the kite she is flying. The string of the kite forms an angle of 27° with the ground. How high in the air is the kite? (1 point)

Question

Responses

98.13 ft.
98.13 ft.

32.18 ft.
32.18 ft.

25.48 ft.
25.48 ft.

22.66 ft.

Answer 1

To find out how high the kite is in the air, we can use trigonometry. Specifically, we can use the sine function because we have the adjacent side (the distance from Kyra to the kite) and we want to find the opposite side (the height of the kite).

Here's the setup:

• \( d \) (the distance from Kyra to the kite) = 50 feet
• \( \theta \) (the angle with the ground) = 27°

We can use the sine function, which is defined as:

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

However, in this scenario, we should actually use cosine since we want the adjacent side:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] But to find the height (opposite side) we should focus on:

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

From this, we get:

\[ \text{height} = \tan(\theta) \times \text{adjacent} \]

Now substituting the values:

\[ \text{height} = \tan(27^\circ) \times 50 \]

Calculating \( \tan(27^\circ) \):

\[ \tan(27^\circ) \approx 0.5095 \]

Now, substituting this back into the height equation:

\[ \text{height} = 0.5095 \times 50 \approx 25.48 , \text{ft} \]

Thus, the height of the kite is approximately 25.48 feet.

Therefore, the correct response is:

25.48 ft.