SOLUTION: Liz is flying a kite. she let out 80 ft of string and attached the string to a stake in the ground, the kite is now directly above her brother mike who is 32 ft away from liz. find

Algebra ->  Pythagorean-theorem -> SOLUTION: Liz is flying a kite. she let out 80 ft of string and attached the string to a stake in the ground, the kite is now directly above her brother mike who is 32 ft away from liz. find      Log On


   

Question 193132: Liz is flying a kite. she let out 80 ft of string and attached the string to a stake in the ground, the kite is now directly above her brother mike who is 32 ft away from liz. find the height of the kite to the nearest foot.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First, let's draw a picture:




We can see that a triangle forms where the legs are "x" and 32 ft with a hypotenuse of 80 ft. To find the unknown length of the leg "x", we need to use the Pythagorean Theorem


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and 32 this means that a=x and b=32


Also, since the hypotenuse is 80, this means that c=80.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B32%5E2=80%5E2 Plug in a=x, b=32, c=80


x%5E2%2B1024=80%5E2 Square 32 to get 1024.


x%5E2%2B1024=6400 Square 80 to get 6400.


x%5E2=6400-1024 Subtract 1024 from both sides.


x%5E2=5376 Combine like terms.


x=sqrt%285376%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=73.321 Evaluate the square root (using a calculator). Note: this value is approximate


Now round to the nearest whole number to get x=73


So the kite is about 73 ft above Mike's head.