Call the hypotenuse of the 60° triangle "y". Then the definition of the sine function tells you
... sin(60°) = (8√2)/y
or (multiplying by y/sin(60°))
... y = (8√2)/sin(60°) = (8√2)/(√3/2) = (16/3)√6
Similarly, the definition of the sine function applied to the larger triangle tells you
... sin(45°) = y/x
or
... x = y/sin(45°) = ((16/3)√6)/(1/√2) = (32/3)√3 . . . . matches selection C.
