Question

I have a trigonometry problem, and I don't know how to solve it. Can somebody show me the steps? "A kit is flying 80ft off the ground, and it's string is pulled taut. The angle of elevation of the kite is 65 degrees. Find the length of the string. Round your answer to the nearest tenth."

Answer 1

88.27 ft

Explanation:

We know that the Kite's length makes a right triangle with the perpendicular height above the ground, 80ft.

-The perpendicular height, 80 ft, corresponds to the angle of elevation, 65°. The kite's length corresponds to 90°.

-Let x be the Kite's length.

-We apply sine rule to calculate the length of the kit:

`(a)/(Sin \ A)=(b)/(Sin \ B)=(c)/(Sin \ C)\\\\(80\ ft)/(Sin \ 65\textdegree)=(x)/(Sin \ 90\textdegree)\\\\x=(80\ ft)/(Sin \ 65\textdegree)\\\\=88.27 \ ft`

Hence, the kite's l;ength is 88.27 ft