Question 193132

First, let's draw a picture:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/work/1.png">



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^2+b^2=c^2}}} 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^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{x^2+32^2=80^2}}} Plug in {{{a=x}}}, {{{b=32}}}, {{{c=80}}} 



{{{x^2+1024=80^2}}} Square {{{32}}} to get {{{1024}}}.



{{{x^2+1024=6400}}} Square {{{80}}} to get {{{6400}}}.



{{{x^2=6400-1024}}} Subtract {{{1024}}} from both sides.



{{{x^2=5376}}} Combine like terms.



{{{x=sqrt(5376)}}} 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.