Question 635440
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:<ul><li>Case 1: The missing side is the hypotenuse. In this case the two sides we know, 2 and {{{sqrt(33)}}} are the legs. Using "h" for the hypotenuse, we can write the equation for the Pythagorean Theorem:
{{{(2)^2+(sqrt(33))^2= (h)^2}}}
Now we solve. First we simplify:
{{{4+33= h^2}}}
{{{37= h^2}}}
Then we find the square root of each side:
{{{sqrt(37) = h}}}</li><li>Case 2: One of the sides we know is the hypotenuse. In this case the hypotenuse must be {{{sqrt(33)}}} since that is bigger than 2 and the hypotenuse is <i>always</i> the largest side. Using "L" for unknown leg, we can set up the Pythagorean Theorem equation:
{{{(2)^2 + (L)^2 = (sqrt(33))^2}}}
Simplifying:
{{{4 + L^2 = 33}}}
Next we subtract 4:
{{{L^2 = 29}}}
And find the square root of each side:
{{{L = sqrt(29)}}}</li></ul>