SOLUTION: If the length of the hypotenuse of a right triangle is 24 meters and the length of one of its legs is 12 meters, find the length of the other leg. Round to the nearest tenth, if ne

Algebra ->  Pythagorean-theorem -> SOLUTION: If the length of the hypotenuse of a right triangle is 24 meters and the length of one of its legs is 12 meters, find the length of the other leg. Round to the nearest tenth, if ne      Log On


   

Question 104465: If the length of the hypotenuse of a right triangle is 24 meters and the length of one of its legs is 12 meters, find the length of the other leg. Round to the nearest tenth, if necessary.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:


Since we can see that the triangle has legs of 12 and x with a hypotenuse of 24, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



12%5E2%2Bx%5E2=24%5E2 Plug in a=12, b=x, and c=24. Now lets solve for x


1+4+4+%2B++x++%5E+2+=+5+7+6 Square each individual term



+x++%5E+2+=+5+7+6+-+1+4+4 Subtract 144 from both sides


+x++%5E+2+=+4+3+2 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+4+3+2+%29 Take the square root of both sides


x=12%2Asqrt%283%29 Simplify the square root


Which approximates to...
x+=+2+0+.+7+8+4+6+0+9+6+9+0+8+2+6+5

So our answer is
x+=+2+0+.+8