1. **Problem Statement:** We are given the expression for $T_{BD}$ as $$T_{BD} = \frac{4.5 \times \cos 10^\circ}{88290 \times 7.6 \times \sin 20^\circ - 88290 \times 12.1 \times \cos 10^\circ}$$ and asked why the term $88290 \times 7.6$ is used for $T_{CE}$ even though the length 12.1 m is from point A. 2. **Understanding the problem:** The terms $7.6$ and $12.1$ represent distances from a reference point (likely point A) to points C and E respectively. The forces or tensions are multiplied by these distances to calculate moments or torques about a pivot. 3. **Formula for moments:** The moment $M$ about a point is given by $$M = F \times d \times \sin \theta$$ where $F$ is the force, $d$ is the perpendicular distance from the pivot to the line of action of the force, and $\theta$ is the angle between the force and the lever arm. 4. **Why multiply by 7.6 for $T_{CE}$:** The distance 7.6 m corresponds to the lever arm length for the force $T_{CE}$, which is the perpendicular distance from the pivot to the line of action of $T_{CE}$. Even if the total length from A to E is 12.1 m, the effective lever arm for $T_{CE}$ is 7.6 m because $T_{CE}$ acts at point C, not E. 5. **Summary:** The multiplication by 7.6 is correct because it represents the moment arm length for $T_{CE}$, which is the distance from the pivot to point C where $T_{CE}$ acts, not the total length to point E. This explains why the term $88290 \times 7.6$ is used for $T_{CE}$ in the moment calculation.