Find x * y in the following figure. The given figure is not to the scale......?

Question

Answer 1

Think △ABC, by the sine law,

x/sin90° = 2/sin(∠ACB)

x*sin(∠ACB) = 2*sin90°

sin(∠ACB) = 2/x

sinθ = sin(180° - θ), so

sin(180° - ∠ACB) = 2/x

sin(∠ACD) = 2/x

Think △ACD, by the sine law,

y/sin(∠ACD) = 3/sin30°

y/(2/x) = 3/(1/2)

xy/2 = 6

xy = 12 <--- the answer