Quinn is flying a kite. The angle of elevation formed by the kite string and the ground is 40°, and the kite string forms a straight segment that is 100 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

Step-by-step explanation:

Quinn, the kite, and the ground form a right triangle where the kite's string represents the hypotenuse of the triangle, the horizontal distance from Quinn and the kite represent one leg of the triangle, and the vertical distance from the kite to the ground represents the final leg of the triangle.

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. For the angle of elevation, the opposite side is equal to the vertical distance between the kite and the ground (what we're being asked to find). Let's call this distance . We have:

Multiply both sides by 100:

Therefore, the vertical distance between the kite and the ground is approximately 64 feet.