Approximate the height of the kite....

Question

A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60° with the horizontal (see the figure). Approximate the height of the kite above level ground if 700 feet of string is payed out. (Round your answer to one decimal place.)

 

_____ ft

Answer 1

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