Kyra is standing 59 feet from the kite she is flying. The string of the kite forms an angle of 27 degrees with the ground. How high in the air is the kite? Round to the nearest hundredths.

Answer 1

To determine the height of the kite, we can use trigonometric functions. The scenario can be represented as a right triangle, where:

• The distance from Kyra to the base of the kite (the ground) is the adjacent side of the triangle.
• The height of the kite is the opposite side.
• The string of the kite is the hypotenuse.

We can use the tangent function, which relates the angle to the opposite and adjacent sides:

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

Here, \(\theta = 27^\circ\), the opposite side is the height of the kite (\(h\)), and the adjacent side is the distance from Kyra to the kite (59 feet). Rearranging the equation to solve for the height (\(h\)) gives us:

\[ h = \tan(27^\circ) \times 59 \]

Now we calculate \(h\):

1. Find \(\tan(27^\circ)\) using a calculator: \(\tan(27^\circ) \approx 0.5095\).

2. Multiply by the distance (59 feet): \[ h = 0.5095 \times 59 \approx 30.0305 \]

Finally, rounding to the nearest hundredths:

\[ h \approx 30.03 \]

So the height of the kite is approximately 30.03 feet.