Question

Suppose you are flying a kite that is 50 feet long. While flying, there is a constant gust of wind that blows the kite to an angle of 60° with the ground. How high, in feet, is the kite above the ground

Answer 1

Height of the kite above the ground = 43.301270189 feet

Explanation:

The illustration above forms a right angled triangle. The right angle triangle have an hypotenuse, adjacent side and opposite sides.

The hypotenuse is given as 50 feet , the angle with the ground is 60°. Using the SOHCAHTOA principle we can find the height of the kite above the ground which is the opposite side .

sine 60° = opposite/hypotenuse

sine 60° = opposite/50

0.8660254038 = opposite/50

cross multiply

opposite = 0.8660254038 × 50

opposite = 43.301270189 feet

Height of the kite above the ground = 43.301270189 feet

The image below is what the illustration forms(right angled triangle)

Answer 2

The kite forms a right angled triangle with hypotenuse of 50 ft. The height of the kite above the ground is the opposite of 60° angle.

Using the sine rule,
Sin 60 = Height of the kite above the ground/Hypotenuse

Therefore,
Height of the kite above the ground = Hypotenuse*Sin 60 = 50 *Sin 60 = 43.3 ft