Question 1192004
let a right triangle represent this situation

the kite string would be the hypotenuse ({{{250}}}ft), 
the base is the horizontal distance ({{{d }}}ft.), and 
the height of the kite would be the triangle's height ({{{h=d+146 }}}ft.)

Using the Pythagorean theorem, you can write:

{{{d^2+(d+146 )^2 =250^2}}}
{{{2 d^2 + 292 d + 21316 = 62500}}}
{{{2 d^2 + 292 d - 41184 = 0}}}........using quadratic formuula we get
{{{d = 88}}}
{{{d = -234}}}->disregard negative solution for distance

height {{{h=(88+146 )ft =234ft}}}