To find the values of a, b and c we can use the trigonometric ratios sine, cosine and tangent.
tanФ=opposite/adjacent
Tan60 = a/6
a = 6×tan60
a = 10.39 = 6√3
cosФ = adjacent/hypotenuse
cos60 = 6/b
b = 6/cos60
b = 12
CosФ = adjacent/hypotenuse
Cos45 = c/12
c = 12cos45
c = 8.49 = 6√2
From the choices given the answer is C. a= 6√3, b=12, and c= 6√2
