Question

Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees

. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

Explanation:

this creates a right-angled triangle 2.5 ft above the ground.

the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.

in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.

so, the height of the kite above ground is

105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.