1. **Problem statement:** Given triangle ABC with sides AB = 10 m, BC = 12 m, AC = 29 m, and angles $\angle A = 49^\circ$, $\angle C = 35^\circ$, find $\angle B$, perimeter $P_\Delta$, and area $A_\Delta$. 2. **Find $\angle B$:** The sum of angles in a triangle is $180^\circ$. $$\angle B = 180^\circ - \angle A - \angle C = 180^\circ - 49^\circ - 35^\circ = 96^\circ$$ 3. **Find perimeter $P_\Delta$:** Sum of all sides. $$P_\Delta = AB + BC + AC = 10 + 12 + 29 = 51\text{ m}$$ 4. **Find area $A_\Delta$:** Use formula $A = \frac{1}{2}ab\sin C$ where $a=AB=10$, $b=BC=12$, and angle between them is $\angle B$ or use Heron's formula. Since given sides are 10, 12, 29, check if triangle is valid: $10 + 12 = 22 < 29$, so triangle cannot exist with these sides. **Conclusion:** Triangle with sides 10, 12, 29 does not satisfy triangle inequality, so no valid triangle exists. **Answer:** $\angle B$ cannot be found, perimeter and area are undefined. --- **Summary:** The given side lengths violate the triangle inequality, so the triangle is not possible.