Problem:
Figure ABCD is a trapezoid with AB∥DC,AB=5,BC=32​, ∠BCD=45∘ and ∠CDA=60∘. The length of DC is
Answer Choices:
A. 7+32​3​
B. 8
C. 921​
D. 8+3​
E. 8+33​
Solution:
Drop perpendiculars from A and B to DC, intersecting DC at F and E, respectively. △BEC is an isosceles right triangle, so BE=EC=3. Since ABEF is a rectangle, FE=5 and AF=3. △AFD is a 30−60−90 triangle, so DF=3​1​AF=3​. So DC=8+3​.
