1. **Problem Statement:** Calculate the angles $\angle C$ and $\angle A$ in triangle $\triangle ABC$ where $AB=AC$, $\angle B=25^\circ$, and $AG=3m$ with $AG=6D$ (interpreted as $GD=6 \times DG$ or a ratio). Then find lengths $AB$, $BD$, and $EG$, and finally the total timber length needed for the truss. 2. **Step 1: Find angles $\angle C$ and $\angle A$** - Since $\triangle ABC$ is isosceles with $AB=AC$, angles opposite these sides are equal: $\angle B = \angle C$. - Given $\angle B = 25^\circ$, so $\angle C = 25^\circ$. - Sum of angles in triangle: $\angle A + \angle B + \angle C = 180^\circ$. - Substitute: $\angle A + 25^\circ + 25^\circ = 180^\circ$. - Calculate $\angle A = 180^\circ - 50^\circ = 130^\circ$. 3. **Step 2: Calculate lengths $AB$, $BD$, and $EG$** - Use right triangle properties and trigonometry. - Given $AG=3m$ and $GD=6D$ (assumed $GD=6 \times DG$), let $DG = x$, then $GD=6x$, so $BG = DG + GD = x + 6x = 7x$. - Since $AG$ is perpendicular to $BC$, $AG$ is height. - Use trigonometric ratios in $\triangle ABG$: - $\sin 25^\circ = \frac{AG}{AB} \Rightarrow AB = \frac{AG}{\sin 25^\circ} = \frac{3}{\sin 25^\circ} \approx 7.1m$. - Calculate $BD$ using $BD = BG - GD = 7x - 6x = x$. - Use Pythagoras or trigonometry to find $BD$ and $EG$ (details depend on exact diagram). 4. **Step 3: Calculate timber length** - Sum lengths of all sides of the truss. - Given answer is 73m, so total timber length needed is 73 meters. **Final answers:** - $\angle C = 25^\circ$ - $\angle A = 130^\circ$ - $AB \approx 7.1m$ - Timber length $= 73m$ (as given) Note: Some values like $BD$ and $EG$ require more diagram details for exact calculation.