SOLUTION: find the measure of b if a = 10 and c = 16 I have figured it out as far as I can, but I am now stuck and I don't know what to do, so if you could put down every single step I woul

Algebra ->  Pythagorean-theorem -> SOLUTION: find the measure of b if a = 10 and c = 16 I have figured it out as far as I can, but I am now stuck and I don't know what to do, so if you could put down every single step I woul      Log On


   

Question 143241: find the measure of b if a = 10 and c = 16
I have figured it out as far as I can, but I am now stuck and I don't know what to do, so if you could put down every single step I would appreciate it!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have a triangle like this set up:


Since we can see that the triangle has legs of 10 and x with a hypotenuse of 16, 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



10%5E2%2Bx%5E2=16%5E2 Plug in a=10, b=x, and c=16. Now lets solve for x


1+0+0+%2B++x++%5E+2+=+2+5+6 Square each individual term



+x++%5E+2+=+2+5+6+-+1+0+0 Subtract 100 from both sides


+x++%5E+2+=+1+5+6 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+1+5+6+%29 Take the square root of both sides


x=2%2Asqrt%2839%29 Simplify the square root



So our answer is x=2%2Asqrt%2839%29 which is approximately x=12.49


So the value of b is b=2%2Asqrt%2839%29 which is approximately b=12.49