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)

Responses

22.66 ft.
22.66 ft.

25.48 ft.
25.48 ft.

98.13 ft.
98.13 ft.

32.18 ft.

1 answer

To find out how high the kite is in the air, we can use trigonometry. Specifically, we'll use the sine function, which relates the angle of a right triangle to the ratio of the opposite side (the height of the kite) to the hypotenuse (the length of the string).

  1. Let \( h \) be the height of the kite.
  2. The angle with the ground is given as \( 27^\circ \).
  3. The length of the string (hypotenuse) can be found using the cosine function, where \( \cos(27^\circ) = \frac{adjacent}{hypotenuse} \).

However, since we need the height, we can use:

\[ \sin(27^\circ) = \frac{h}{50} \]

Now, we can rearrange this to solve for \( h \):

\[ h = 50 \cdot \sin(27^\circ) \]

Using a calculator to find \( \sin(27^\circ) \):

\[ \sin(27^\circ) \approx 0.4540 \]

Now substitute that value into the equation:

\[ h \approx 50 \cdot 0.4540 \approx 22.7 \text{ ft} \]

So the height of the kite is approximately 22.66 ft.

The correct answer is: 22.66 ft.