1. Determine the length of side \(r\) of triangle \(PQR\). Round to the nearest hundredth.

    Note that the hypotenuse is side \(q\).

    \(\begin{align}
     p^2 + r^2 &= q^2  \\
     \left( {15} \right)^2 + r^2 &= \left( {20} \right)^2  \\
     225 + r^2 &= 400 \\
     r^2 &= 175 \\
     r &= \sqrt {175}  \\
     r &= 13.228... \\
     r &\doteq 13.23{\rm \thinspace{mm}} \\
     \end{align}\)



  2. Determine the length of side \(v\) of triangle \(UVW\). Round to the nearest hundredth.

    Note that the hypotenuse is side \(v\).

    \(\begin{align}
     u^2 + w^2 &= v^2  \\
     \left( 6 \right)^2 + \left( {10} \right)^2 &= v^2  \\
     36 + 100 &= v^2  \\
     136 &= v^2  \\
     \sqrt {136} &= v \\
     11.661... &= v \\
     11.66{\rm \thinspace{m}} &\doteq v \\
     \end{align}\)