Question

A man flies a kite with a 100 foot string. The angle of elevation of the string is 52°. How high off the ground is the kite?

Answer 1

The kite is approximately 78.80 feet off of the ground.

Explanation:

If we assume that the string his held taut without any swag, we can use a right triangle to solve for the height of the kite.

For this triangle with a reference angle of `52^o`, the hypoteneuse is `100ft` and the `h` is the height on the opposite side of the triangle from the reference angle.

Sine of an angle is the ratio of the opposite side over the hypotenuese.

`Sintheta = (opp)/(hyp)`

`sin52^o = h/(100ft)`

`100sin52^o = h`

`100(0.7880) = h`

`78.80ft =h`