Solve for the unknown sides of the given triangle. Whats a and c?

Question

Answer 1

Rotate so 27 side is parallel with y-axis and a side a on top of positive x-axis. angle 60 degrees is at origin of xy axis. I know sin(60 degrees)=(√3)/2 when hypotenuse is 1 so

c*sin(60)=27 ( hypontense*sin(angle)=opposite side)

c=54/(√3)

a =c* cos(*60) (hypontenuse*cos(angle)=adjacent side)

I know cos(60 degrees)=1/2

a=27/(√3)

let's check, I know "x²+y²=h²" for right triangle

does 27²+(27/√3)²=(54/√3)²

(54/√3)²=54²/3

and

27²+(27/√3)² = 27²(1+1/3) =27²*(4/3) = 27²*2²/3 = 54²/3