You are flying a kite and have led out 80 m of string. The kite angle of elevation with the ground is 40° if the string is stretched straight how high is the kite above the ground?
To find the height of the kite, we can use the trigonometric function tangent.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the kite (h) and the adjacent side is the distance from the kite to the point on the ground directly below it (80 m).
Let's call the height of the kite h.
We know that the tangent of the angle of elevation (40°) is equal to h/80.
Using the tangent function, we can calculate the height of the kite:
tan(40°) = h/80
To isolate h, we multiply both sides of the equation by 80:
80 * tan(40°) = h
Using a calculator, we can calculate the tangent of 40°:
tan(40°) ≈ 0.8391
Now, we can substitute this value back into the equation:
80 * 0.8391 ≈ 67.128
Therefore, the height of the kite above the ground is approximately 67.128 m.