How Do You Calculate Tension and Hinge Forces in Static Equilibrium?

[lightonahill7]

Homework Statement

The metal pole has a mass of 10kg, and the load has a mass of 50kg. The rope is attached so that it is ¼ of the pole’s length from the free end of the pole. Find the tension in the rope and the force at the hinge.

Homework Equations

The Attempt at a Solution

 

[lightonahill7]

I have tried to set up this problem but would like some feedback.

I want to set my vector diagram with the origin placed at the hinge point, with y+ upwards and x+ going to the right.

$$\sum$$ $$\tau$$=0

T(3/4)sin20 - 98N(1/2)sin50 - 490(1)sin50 = 0

T(3/4)sin20 = 412.8979548

T = 188.29 N

If I am right with the value for tension, then to find x and y components of force would be:

$$\sum$$ F_y = 0

A_y - 98 - 490 + 188.29sin20 = 0

A_y = 523.7 N

$$\sum$$ F_x = 0

A_x - 188.29cos20 = 0

A_x = 176.93 N

Am I on the right track?