Question

Luis is flying a kite, holding his hands a distance of 3.75 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 35^{\circ} ∘ . If the string from the kite to his hand is 140 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

The height of the kite above the ground to the nearest tenth of a foot is 84.1 ft

Using the angle of elevation to find height?

The situation forms a right angle triangle.

Therefore, the length of the string is the hypotenuse of the triangle formed.

Hence, using trigonometric ratios,

sin 35 = opposite / hypotenuse

sin 35 = h / 140

cross multiply

h = 140 sin 35

h = 140 × 0.57357643635

h = 80.3007010891

Height of the kite above the ground = 80.3007010891 + 3.75 = 84.0507010891

Height of the kite above the ground = 84.1 ft

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