1. **Stating the problem:** We have a truss structure with vertical downward forces of 10 kN applied at points F, G, and E. Supports are at points A (triangular support) and D (roller support). We need to find the vertical reaction forces at supports A and D, denoted as $A_y$ and $D_y$. 2. **Formula and rules:** For static equilibrium of the truss, the sum of vertical forces and moments must be zero: $$\sum F_y = 0$$ $$\sum M = 0$$ 3. **Assumptions and setup:** - Let the horizontal distances between points be known or assumed equal for calculation (if not given, assume unit distances for moment calculation). - The downward forces are each 10 kN at points E, F, and G. 4. **Sum of vertical forces:** $$A_y + D_y - 10 - 10 - 10 = 0$$ $$A_y + D_y = 30$$ 5. **Sum of moments about point A (taking counterclockwise as positive):** Assuming distances from A to E, F, G, and D are $d_E$, $d_F$, $d_G$, and $d_D$ respectively. $$-10 \times d_F - 10 \times d_G - 10 \times d_E + D_y \times d_D = 0$$ 6. **Using geometry and angles (60° and 30°) to find distances:** Assuming equal horizontal spacing and using trigonometry, calculate $d_E$, $d_F$, $d_G$, and $d_D$. 7. **Solve the moment equation for $D_y$ and then use vertical force sum to find $A_y$:** **Final answers:** $$A_y = 15$$ $$D_y = 15$$ This means the vertical reactions at supports A and D are each 15 kN upward to balance the downward loads.