Question 1185801
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The information describes a right triangle with legs x (along the ground) and x+82 (the height above the ground) and a hypotenuse (the kite string) of 170.<br>
Use the Pythagorean Theorem: {{{c^2=a^2+b^2}}}<br>
{{{x^2+(x+82)^2=170^2}}}<br>
That gives a quadratic equation that you can solve to find x and then find the height.<br>
The numbers are large enough that solving by factoring, or even using the quadratic formula, is messy.  I would graph the two functions {{{x^2+(x+82)^2)}}} and {{{170^2}}} with a graphing calculator and find where they intersect.<br>
{{{graph(400,400,-20,100,-5000,50000,x^2+(x+82)^2,170^2)}}}<br>
The graphs intersect at x=72, so<br>
ANSWER: the height of the kite is 72+82=154 feet<br>