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Chee is flying a kite, holding her hands a distance of 3.25 feet above the ground and
letting all the kite's string play out. She measures the angle of elevation from her hand to the kite to be 29º. If the string from the kite to her hand is 100 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Sagot :

oladayoademosu

The height of the kite above the ground is 58.68 ft

Let x be the height of the kite above Chee's hand.

The height of the kite above Chee's hand, the string and the horizontal distance between Chee and the kite form a right angled triangle with hypotenuse side, the length of the string and opposite side the height of the kite above Chee's hand.

Since we have the angle of elevation from her hand to the kite is 29°, and the length of the string is 100 ft.

From trigonometric ratios, we have

tan29° = x/100

So, x = 100tan29°

x = 100 × 0.5543

x = 55.43 ft.

Since Chee's hand is y = 3.25 ft above the ground, the height of the kite above the ground, L = x + y

= 55.43 ft + 3.25 ft

= 58.68 ft to the nearest hundredth of a foot

So, the height of the kite above the ground is 58.68 ft

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