Question

You are holding a kite string in your hand. The angle of elevation from your hand to the kite is 57⁰ and the distance to the kite is 300 feet. Your hand is 5 feet above the ground. How high is the kite? Round your answer to the nearest tenth of a foot. ​

Answer 1

256.6 feet

Explanation:

First, I recommend drawing a picture for problems like this. See attached for my example!

-> What does the "angle of elevation" mean? In summary, if your hand has a line going out in both directions horizontally from it, it is the angle "up" to the kite.

Now, let us find out what formula(s) we will use to solve this problem.

-> We have two of the angles (so we can easily find the third) as well as the hypotenuse

-> We are solving for one of the legs, then adding five feet to it

-> I think I will use the 57° angle and the sine function since we have the hypotenuse and are solving for the opposite side (to the angle 57°)

Lastly, we will solve! First, I will find the length of the opposite side to the 57° angle.

sin(θ) =
`(opposite)/(hypotenuse)`

sin(57°) =
`(x)/(300)`

300sin(57°) = x

251.6 ≈ x

x ≈ 251.6 feet

Now we will add 5 feet to 251.6 since your hand is 5 feet above the ground.

251.6 + 5 = 256.6