SOLUTION: In a right triangle, find the length of the side not given b=2, c=√33 The length of the third side is

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Question 635440: In a right triangle, find the length of the side not given b=2, c=√33
The length of the third side is
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
From what you posted it is not possible to know if the hypotenuse is the missing side or one of the sides you were given. (Perhaps there was a diagram with the problem that showed you which side was the hypotenuse. Without knowing this, there are two possible solutions:
  • Case 1: The missing side is the hypotenuse. In this case the two sides we know, 2 and sqrt%2833%29 are the legs. Using "h" for the hypotenuse, we can write the equation for the Pythagorean Theorem:
    %282%29%5E2%2B%28sqrt%2833%29%29%5E2=+%28h%29%5E2
    Now we solve. First we simplify:
    4%2B33=+h%5E2
    37=+h%5E2
    Then we find the square root of each side:
    sqrt%2837%29+=+h
  • Case 2: One of the sides we know is the hypotenuse. In this case the hypotenuse must be sqrt%2833%29 since that is bigger than 2 and the hypotenuse is always the largest side. Using "L" for unknown leg, we can set up the Pythagorean Theorem equation:
    %282%29%5E2+%2B+%28L%29%5E2+=+%28sqrt%2833%29%29%5E2
    Simplifying:
    4+%2B+L%5E2+=+33
    Next we subtract 4:
    L%5E2+=+29
    And find the square root of each side:
    L+=+sqrt%2829%29