Question

Quinn is flying a kite. The angle of elevation formed by the kite string and the ground is 46°, and the kite string forms a straight segment that is 80 feet long.
Explain how to find the distance between the ground and the kite. Include a description of the triangle you drew to help you solve, including the variables and measurements you assigned to each side and angle. Round your answer to the nearest foot.

Answer 1

Answer:  58 feet

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Check out the diagram below.

We have a right triangle such that the vertical leg is unknown. We'll call it x. This is opposite the reference angle 46°

The hypotenuse is the length of the string, which is 80 ft.

We use the sine ratio to tie the opposite and hypotenuse together.

sin(angle) = opposite/hypotenuse

sin(46) = x/80

80*sin(46) = x

x = 80*sin(46)

x = 57.54718 approximately

x = 58 feet

The kite is 58 feet off the ground.

For comparison, a 6 story building is 6*10 = 60 ft tall, assuming each story is 10 ft tall. So this kite is about 2 feet short of the top of the building.

Edit: I changed 56 to 58