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)

Answer 1

To find out how high the kite is in the air, we can use some trigonometry. We know the following:

- The distance Kyra is standing from the kite (ground distance) is 50 feet.
- The angle the string of the kite makes with the ground is 27°.

We're looking for the height of the kite, which we can represent as the opposite side of the right triangle formed by the ground distance and the string of the kite. We can use the tangent function, which relates the opposite side and the adjacent side in a right triangle:

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

In this case, \(\theta = 27^\circ\), the opposite side is the height of the kite (h), and the adjacent side is the distance from Kyra to the kite (50 feet):

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

Now, we can solve for \(h\):

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

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

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

Now substituting that value back into the equation:

\[
h \approx 50 \cdot 0.5095 \approx 25.475
\]

So, the height of the kite is approximately **25.5 feet**.