Question 208678
The 3 sides of <b>every</b> right triangle must fit the equation from the Pythagorean Theorem: {{{a^2 + b^2 = c^2}}}. The only "trick" is to understand that the hypotenuse, since it is always the longest side, must be the "c" in the equation. (It makes no difference which leg is "a" and which leg is "b".)<br>
So we'll make the 3-inch leg "a" and the hypotenuse must be "c":
{{{(3)^2 + b^2 = (4)^2}}}
Now we just solve this to find "b", the other leg. Start by simplifying:
{{{9 + b^2 = 16}}}
Subtract 9 from both sides:
{{{b^2 = 7}}}
Find the square root of both sides:
{{{sqrt(b^2) = sqrt(7)}}}
{{{abs(b) = sqrt(7)}}}
{{{b = sqrt(7)}}} or {{{b = -sqrt(7)}}}
Since "b" represents the side of a triangle, we reject the negative solution. So the answer is that the third side of the triangle has a length of {{{sqrt(7)}}}.