Question

The Tangent Ratio Quick Check 2 of 52 of 5 Items Question 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 32.18 ft. 32.18 ft. 25.48 ft. 25.48 ft. 98.13 ft. 98.13 ft. 22.66 ft. 22.66 ft. Skip to navigation page 8 of 8

Answer 1

To find the height of the kite, we can use the tangent ratio since we have the angle and the distance from Kyra to the kite.

The formula for the tangent of an angle in a right triangle is:

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

In this scenario:
- The angle \( \theta \) is 27°.
- The adjacent side (distance from Kyra to the kite) is 50 feet.
- The opposite side (height of the kite) is what we want to find.

Rearranging the formula gives us:

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

Plugging in the values:

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

Calculating \( \tan(27°) \):

Using a calculator:
- \( \tan(27°) \approx 0.5095 \)

Now plug it in:

\[
\text{height} \approx 0.5095 \times 50 \approx 25.475 \text{ ft}
\]

Rounding this:

\[
\text{height} \approx 25.48 \text{ ft}
\]

Therefore, the height of the kite is approximately **25.48 ft**.