Using the side ratios for 30-60-90s and 45-45-90s, you know that
and that
Therefore,
The answer is (D).
HIDDEN SPECIAL TRIANGLES
It happens a lot that the key to solving a geometry problem is to add a line
segment or two to the figure. Often what results is one or more special
triangles. The ability to spot, even to create, special triangles comes in handy
in a question like Example 4.
Example 4