Help calculating the moment of a system!?

The easiest way for such question is find the equation of the line at which force is acting, then find perpendicular distance of point from given line using d = |ax(o) + by(o) + c| / √(a²+b²)

We know the slope of point P = 3/4, and

we can find the co-ordinate of point P asx = 3 cos30, and y = 3 sin 30

Now eqn of a line passing through point P and having slope m = 3/4

y = (3/4)x + c ; plug value of x and y, you find c = (12 - 9√3)/8

now find the vertical distance of point D (0, -2) from line which is 3x - 4y + (12 - 9√3)/2 = 0

d = |ax(o) + by(o) + c| / √(a²+b²) ; where x(o) = 0, y(o) = -2

d = |0 + 8 + 6 - 4.5√3| / √(3²+4²)

d = 1.2411 meter

Moment about point D for force P = Force (P) * Perpendicular distance (d) = 37234.6 N-m

Hope this helped

Vick