SOLUTION: A kite is flying on 52 feet of string. How high is it above the ground if it's height is 28 feet more than the horizontal distance from the person flying it? Assume the string is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A kite is flying on 52 feet of string. How high is it above the ground if it's height is 28 feet more than the horizontal distance from the person flying it? Assume the string is       Log On


   

Question 210174: A kite is flying on 52 feet of string. How high is it above the ground if it's height is 28 feet more than the horizontal distance from the person flying it? Assume the string is being released at ground level.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2%2B%28d%2B28%29%5E2+=+52%5E2
d%5E2%2B%28d%5E2%2B56d%2B784%29+=+2704 Simplify.
2d%5E2%2B56d%2B784+=+2704 Subtract 2704 from both sides.
2d%5E2%2B56d-1920+=+0 Divide through by 2.
d%5E2%2B28d-960+=+0 Factor.
%28d-20%29%28d%2B48%29+=+0 so that...
d+=+20 or d+=+-48 Discard the negative solution.
d+=+20feet
So the height of the kite is:
h+=+d%2B28
h+=+20%2B28
highlight%28d+=+48%29feet.