Question

You go to the park on a windy day to fly a kite. You have released 40 feet of string. The string makes an angle of 30°with the ground. How high is the kite in the air?

Answer 1

To solve this problem, we can use trigonometry. Let's assume that the height of the kite from the ground is h. Then, we can use the tangent function to find the value of h.

We know that the tangent of an angle is equal to the opposite side over the adjacent side. In this case, the opposite side is the height of the kite (h) and the adjacent side is the distance from you to the point directly below the kite on the ground, which is 40 feet.

So we have:

tan(30°) = h/40

Multiplying both sides by 40, we get:

h = 40 tan(30°)

Using a calculator, we can find the value of tangent of 30 degrees, which is approximately 0.5774. So:

h = 40 × 0.5774 ≈ 23.1

Therefore, the height of the kite in the air is approximately 23.1 feet.

Answer 2

20 feet

Explanation:

You can use trigonometry to solve this problem. The height of the kite can be found using the sine function. The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

In this case, the side opposite the 30° angle is the height of the kite (h), and the hypotenuse is the length of the string (40 feet). So we have:

sin(30°) = h / 40

Solving for h, we get:

h = 40 * sin(30°)

Since sin(30°) = 0.5, we have:

h = 40 * 0.5

So, h = 20 feet.

The kite is 20 feet high in the air.