A boy flying a kite lets out 60ft of string. If the angle of elevation to the kite is 17°, how high above the ground is the kite
sin 17 = h/60
To find the height above the ground at which the kite is flying, we can use trigonometry.
Let's assume that the height of the kite above the ground is represented by 'h'.
In this case, the angle of elevation, 17°, represents the angle between the horizontal ground and the line connecting the boy to the kite.
We can create a right triangle with the string of the kite as the hypotenuse, the height of the kite as the opposite side, and the horizontal distance from the boy to the kite as the adjacent side.
Using the trigonometric ratio tan(theta) = opposite/adjacent, we have:
tan(17°) = h/60ft
To find the height, h, we can rearrange the equation:
h = tan(17°) * 60ft
Calculating the value, we have:
h ≈ 17 * 60ft / 100
h ≈ 10.2ft
Therefore, the kite is flying at a height of approximately 10.2 feet above the ground.
To find the height of the kite above the ground, we need to use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the height and the distance.
Let's break down the information given in the problem:
- The boy lets out 60ft of string. This is the distance between the boy and the kite, which we'll call the hypotenuse of the right triangle.
- The angle of elevation to the kite is 17°. This is the angle between the ground and the hypotenuse.
To find the height of the kite, we need to use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the opposite side is the height of the kite above the ground, and the adjacent side is the distance between the boy and the kite.
Using the tangent function:
tan(17°) = height / 60ft
To solve for the height, we can rearrange the equation:
height = tan(17°) * 60ft
Calculating the value:
height ≈ 0.3002 * 60ft
height ≈ 18.01ft
Therefore, the kite is approximately 18.01ft above the ground.