The two legs of a right triangle are \( m \) and n . The hypotenuse is p . Solve for m in terms of the other variables.

To solve for \( m \) in terms of \( n \) and \( p \) in a right triangle, we can use the Pythagorean theorem, which states that \( p^2 = m^2 + n^2 \). Rearranging this equation to isolate \( m \), we have \( m^2 = p^2 - n^2 \). Taking the square root of both sides results in \( m = \sqrt{p^2 - n^2} \). Voilà! You've found \( m \) in all its geometric glory! Now, keep in mind that since we're dealing with lengths, \( m \) must always be positive, so when applying this formula in real situations, check your values for \( p \) and \( n \) to ensure that \( p \) is greater than \( n \) (because the hypotenuse is always the longest side). It’s all about keeping those triangles in check!