What is the value of x? the figure shows 2 right triangles, triangle a b c with right angle b and triangle b d c with right angle d. the measure of angle b a c is 45 degrees. the measure of angle d b c is 60 degrees. the length of side c a is 6 square root 2. the length of side b d is x. enter your answer in the box. x =

Triangle ABC has:
∡ABC = 90°
∡BAC = 45°
Therefore also ∡BCA = 45° 
This means that ABC is isosceles and that each leg is:
l = √2/2 · h
Since the hypotenuse of ABC is AC = 6√2
BC = √2/2 · 6√2 = 6

Now, consider the triangle BCD:
∡BDC = 90°
∡DBC = 60°
which means that: ∡BCD = 30°
In such triangles, the side opposite to the angle of 30° is 1/2 · h
Since the hypotenuse is BC = 6, we have:
BD = 1/2 · 6 = 3

Hence, x = 3

38 dollars is your answer.