Exercise 5 Page 514

Notice that the given right triangle has a marked angle measuring $30^{\circ }.$ Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be $60^{\circ }.$

In a $30^{\circ }\text{-}60^{\circ }\text{-}90^{\circ }$ triangle, the longer leg is $\sqrt{3}$ times the length of the shorter leg. We found that the measure of the longer leg is $6.$ Also, in a $30^{\circ }\text{-}60^{\circ }\text{-}90^{\circ }$ triangle, the hypotenuse is $2$ times the length of the shorter leg.