You can work out c first. That's probably the key to the whole problem.
The adjacent side to a 60o angle is 1/2 the hypotenuse
The hypotenuse in this case = 4 Sqrt(3)
Then c = 1/2 (4 sqrt(3))
c = 2 sqrt(3) That means d is not true.
Next work out a.
a is in the same triangle as c and the hypotenuse.
a^2 + c^2 = hypotenuse^2
a = ??
c = 2 sqrt(3)
h = 4 sqrt(3)
a^2 + (2 sqrt(3))^2 = (4 sqrt(3))^2
(sqrt(3))^2 = 3
a^2 + 4 * 3 = 16 * 3
a^2 + 12 = 48
a^2 = 48 - 12
a^2 = 36
a = 6
Now we need to work out d
The side opposite and the side adjacent are equal when opposite a 45o angle in a right angle triangle
d = 6
The last thing to work out is be
a = 6
d = 6
c = ???
a^2 + d^2 = c^2
6^2 + 6^2 = c^2
c^2 = 72
c = sqrt(72)
c = sqrt(6*6*2)
c = 6 sqrt(2)
The answer should be B??? Check this out.