Kyra is standing 50 feet from the kite she is flying. The string of the kite forms an angle of 27°

27
°
with the ground. How high in the air is the kite? (1 point)
Responses

22.66 ft.
22.66 ft.

98.13 ft.
98.13 ft.

32.18 ft.
32.18 ft.

25.48 ft.

1 answer

To find the height of the kite in the air, we can use trigonometry, specifically the sine function. The height of the kite forms the opposite side of the right triangle, with the distance from Kyra to the kite (50 feet) being the adjacent side and the angle being 27°.

Using the formula: \[ \text{Height} = \text{adjacent} \times \tan(\text{angle}) \]

Here, the opposite side (height) is what we want, and the adjacent side is the distance from Kyra to the kite:

\[ h = 50 \times \tan(27°) \]

Calculating the height:

  1. Calculate \(\tan(27°)\).
  2. Then multiply the result by 50.

Using a calculator:

\[ \tan(27°) \approx 0.5095 \]

Now calculating the height:

\[ h = 50 \times 0.5095 \approx 25.475 \text{ feet} \]

Rounding to two decimal places, the height is approximately:

\[ 25.48 \text{ feet} \]

Therefore, the answer is 25.48 ft.