SOLUTION: Please, i need your help to understand how to solve the measurement of the hypotenuse. I understand a^2+b^2=c^6, but i dont understand how to solve for a missing side when rational

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: Please, i need your help to understand how to solve the measurement of the hypotenuse. I understand a^2+b^2=c^6, but i dont understand how to solve for a missing side when rational      Log On

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Question 175482: Please, i need your help to understand how to solve the measurement of the hypotenuse. I understand a^2+b^2=c^6, but i dont understand how to solve for a missing side when rationalized into a radical.
for example, a=18 b=? c=33
i know it should be 324+b^2=1089
-324
b^2=765
but what do i do next?
i would greatly appreciate it if you helped me. thank you.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up (note: you can rearrange the triangle):


drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C18%29%2C%0D%0Alocate%281%2C-0.2%2Cx%29%2C%0D%0Alocate%281%2C2%2C33%29%0D%0A%29


Since the legs are 18 and x this means that a=18 and b=x


Also, since the hypotenuse is 33, this means that c=33.


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


18%5E2%2Bx%5E2=33%5E2 Plug in a=18, b=x, c=33


324%2Bx%5E2=33%5E2 Square 18 to get 324.


324%2Bx%5E2=1089 Square 33 to get 1089.


x%5E2=1089-324 Subtract 324 from both sides.


x%5E2=765 Combine like terms.


x=sqrt%28765%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=3%2Asqrt%2885%29 Simplify the square root. (note: If you need help with simplifying square roots, check out this solver)


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Answer:


So the solution is x=3%2Asqrt%2885%29 which approximates to x=27.659.