1. **Problem Statement:** We are given measurements of heights ($h_A$, $h_B$, $h_C$, $h_D$), lengths ($L_1$, $L_2$, $L_3$), and weights ($W$) along with theoretical and experimental forces. We need to calculate angles $a_1$, $a_2$, $a_3$ using the sine inverse function and compare theoretical and experimental forces using the method of joints. 2. **Formulas and Rules:** - Calculate height differences: $h_1 = h_A - h_B$, $h_2 = h_B - h_C$, $h_3 = h_B - h_C$. - Calculate angles: $a_i = \sin^{-1}\left(\frac{h_i}{L_i}\right)$ for $i=1,2,3$. - Use method of joints to solve for forces in members by applying equilibrium equations: - Sum of forces in $x$ and $y$ directions must be zero. - $\sum F_x = 0$, $\sum F_y = 0$. 3. **Calculations for the first table (W=14 N):** - Given: $h_A=525$, $h_B=320$, $h_C=150$, $L_1=520$, $L_2=500$. - Compute $h_1 = 525 - 320 = 205$ mm. - Compute $h_2 = 320 - 150 = 170$ mm. - Calculate angles: $$a_1 = \sin^{-1}\left(\frac{205}{520}\right) = 23.218^\circ$$ $$a_2 = \sin^{-1}\left(\frac{170}{500}\right) = 19.877^\circ$$ 4. **Calculations for the second table (W=15 N):** - Given: $h_A=525$, $h_B=315$, $h_C=150$, $h_D=250$, $L_1=470$, $L_2=450$, $L_3=410$. - Compute height differences: $$h_1 = 525 - 315 = 210$$ $$h_2 = 315 - 150 = 165$$ $$h_3 = 315 - 250 = 65$$ - Calculate angles: $$a_1 = \sin^{-1}\left(\frac{210}{470}\right) = 26.539^\circ$$ $$a_2 = \sin^{-1}\left(\frac{165}{450}\right) = 21.51^\circ$$ $$a_3 = \sin^{-1}\left(\frac{65}{410}\right) = 9.122^\circ$$ 5. **Method of Joints for Forces:** - Use equilibrium equations at each joint to solve for unknown forces $F_1$, $F_2$, $F_3$. - Compare theoretical forces ($F_{th}$) with experimental forces ($F_{exp}$). - Calculate differences and percentage errors: $$\Delta F = F_{th} - F_{exp}$$ $$\Delta F\% = \frac{\Delta F \times 100}{F_{th}}$$ 6. **Summary:** - Angles $a_1$, $a_2$, $a_3$ are calculated using sine inverse of height differences over lengths. - Forces are compared between theoretical and experimental values with percentage differences. - This approach helps validate the experimental setup against theoretical predictions using the method of joints. **Final angles for W=15 N:** $$a_1 = 26.539^\circ,\quad a_2 = 21.51^\circ,\quad a_3 = 9.122^\circ$$