Determine the horizontal component of reaction at pin C. Set F1 = 400 lb and F2 = 350 lb. Determine the vertical component of reaction at pin C.

## Answer

## General guidance

Write the equilibrium equations.
Here, the resultant moment about any arbitrary point is .
Calculate the magnitude of force using the trigonometric relation:

Here, the component of force in *x*-direction is and the component of force in *y*-direction is .
**Sign Convention for force**:** **Upward and right forces are positive.
**Sign convention for moment**: Anti clockwise moment is positive and clockwise moment is negative.

## Step-by-step

### Step 1 of 4

Draw the free body diagram of the system.

Draw the external forces acting on the system and Reaction forces. At point *C*, the joint is pinned. Hence, there will be all two reactions . *AB* is a two force member and hence force acts along member *AB*.

### Step 2 of 4

Take moment about point *C*.

Apply the moment equilibrium at point *C* to calculate the force in the two force member *AB*.

### Step 3 of 4

Apply equations of equilibrium in *x*-direction.

The horizontal reaction force at point *C *is .

Calculation of reaction force at point *C* in horizontal direction using the equilibrium conditions about *x*-axis.

### Step 4 of 4

Apply equations of equilibrium in *y*-direction.

The vertical reaction force at point *C *is .

Calculation of reaction force at point *C* in horizontal direction using the equilibrium conditions about *y*-axis.

### Answer

The horizontal reaction force at point *C *is .

The vertical reaction force at point *C *is .

### Answer only

The horizontal reaction force at point *C *is .

The vertical reaction force at point *C *is .