SOLUTION: A kite is flying on 250 feet of string. How high is it above the ground if its height is 146 feet more than the horizontal distance from the person flying​ it? Assume the string

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A kite is flying on 250 feet of string. How high is it above the ground if its height is 146 feet more than the horizontal distance from the person flying​ it? Assume the string       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1192004: A kite is flying on 250 feet of string. How high is it above the ground if its height is 146 feet more than the horizontal distance from the person flying​ it? Assume the string is being released at ground level.
The kite is _____ ft above the ground.
Thanks for your help!(:
Found 2 solutions by math_tutor2020, MathLover1:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Draw out a right triangle with the following properties:
  • a = horizontal leg = x
  • b = vertical leg = height = x+146 (since it's 146 feet longer than the horizontal side)
  • c = hypotenuse = 250 ft string
We'll need the pythagorean theorem to tie together the three sides mentioned.
The goal is to find x, and then use that to compute x+146 to get the height.

a%5E2+%2B+b%5E2+=+c%5E2

x%5E2+%2B+%28x%2B146%29%5E2+=+250%5E2

x%5E2+%2B+%28x%2B146%29%28x%2B146%29+=+250%5E2

x%5E2+%2B+x%5E2%2B146x%2B146x%2B146%5E2+=+250%5E2

2x%5E2%2B292x%2B21316+=+62500

2x%5E2%2B292x%2B21316-62500=0

2x%5E2%2B292x-41184=0

Next, apply the quadratic formula.
We'll use a = 2, b = 292, c = -41184
x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28292%29%2B-sqrt%28%28292%29%5E2-4%282%29%28-41184%29%29%29%2F%282%282%29%29

x+=+%28-292%2B-sqrt%28414736%29%29%2F%284%29

x+=+%28-292%2B-+++644%29%2F%284%29

x+=+%28-292%2B644%29%2F%284%29 or x+=+%28-292-644%29%2F%284%29

x+=+%28352%29%2F%284%29 or x+=+%28-936%29%2F%284%29

x+=+88 or x+=+-234
Negative lengths or distances don't make sense, so we ignore the negative x value.

We only focus on x+=+88 and it leads to x%2B146+=+88%2B146+=+highlight%28234%29

Answer:
The kite is 234 feet in the air

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let a right triangle represent this situation
the kite string would be the hypotenuse (250ft),
the base is the horizontal distance (d+ft.), and
the height of the kite would be the triangle's height (h=d%2B146+ft.)
Using the Pythagorean theorem, you can write:
d%5E2%2B%28d%2B146+%29%5E2+=250%5E2
2+d%5E2+%2B+292+d+%2B+21316+=+62500
2+d%5E2+%2B+292+d+-+41184+=+0........using quadratic formuula we get
d+=+88
d+=+-234->disregard negative solution for distance
height h=%2888%2B146+%29ft+=234ft