Question 210174
You can let a right triangle represent this situation.
The kite string would be the hypotenuse (52ft.), the base is the horizontal distance (d ft.), and the height of the kite would be the triangle's height (d+28 ft.).
Using the Pythagorean theorem, you can write:
{{{d^2+(d+28)^2 = 52^2}}}
{{{d^2+(d^2+56d+784) = 2704}}} Simplify.
{{{2d^2+56d+784 = 2704}}} Subtract 2704 from both sides.
{{{2d^2+56d-1920 = 0}}} Divide through by 2.
{{{d^2+28d-960 = 0}}} Factor.
{{{(d-20)(d+48) = 0}}} so that...
{{{d = 20}}} or {{{d = -48}}} Discard the negative solution.
{{{d = 20}}}feet
So the height of the kite is:
{{{h = d+28}}}
{{{h = 20+28}}}
{{{highlight(d = 48)}}}feet.