Akite has a string tired to its center. the kite is let out on 90ft of the string and the other end of the string is held at 4ft above the ground. from where the string is held, the angle of elevation to the center of the kite is 40°. if you maintain the same angle of elevation from where the string is held, how much more string would you need to let out for the kite to fly 10ft higher? round to the nearest tenth of a foot.

Step-by-step explanation: We want the vertical height of the kite above level ground.  We are given the angle (θ) and the length of string (hypotenuse, c).  We want to find the opposite side (b) and add it to 4 ft.

The height above the kite holder's hand is 4 feet.  We have for the total height,

y = b + 4 ft

opposite/hypotenuse = b/c = sin(θ)   →   b = c sin(θ)

Substituting into the first equation,

y = 700 ft sin(60°) + 4 ft = 610.2 ft