Question

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

a. 98.13 ft.
b. 22.66 ft.
c. 25.48 ft.
d. 32.18 ft.

Answer 1

To find the height of the kite, we can use the trigonometric function tangent, which is defined as the ratio of the opposite side (height of the kite) to the adjacent side (distance from Kyra to the kite).

Given:
- Distance from Kyra to the kite (adjacent side) = 50 feet
- Angle of the string with the ground = 27 degrees

We can use the formula:

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

Where:
- \(\theta\) is the angle (27 degrees),
- opposite is the height of the kite (h),
- adjacent is the distance from Kyra to the kite (50 feet).

Rearranging the formula to solve for \(\text{opposite}\):

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

Substituting the values:

\[
h = \tan(27^\circ) \times 50
\]

Now, we can calculate \(\tan(27^\circ)\):

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

Now plug this value into the equation:

\[
h \approx 0.5095 \times 50
\]

\[
h \approx 25.475 \text{ feet}
\]

Rounding this to two decimal places gives us:

\[
h \approx 25.48 \text{ feet}
\]

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

The correct answer is **c. 25.48 ft.**