1. **Stating the problem:** We need to find the volume of a triangular pyramid (tetrahedron) with given edge lengths: base triangle sides 8 cm and 3 cm (height), and adjacent faces with edges 5 cm, 5 cm, and 7 cm. 2. **Understanding the shape:** The base is a triangle with base $b=8$ cm and height $h=3$ cm. The area of the base triangle is given by the formula: $$\text{Area}_{base} = \frac{1}{2} \times b \times h$$ 3. **Calculate the base area:** $$\text{Area}_{base} = \frac{1}{2} \times 8 \times 3 = 12 \text{ cm}^2$$ 4. **Finding the height of the pyramid:** The height of the pyramid is the perpendicular distance from the apex to the base plane. Given the adjacent faces with edges 5 cm, 5 cm, and 7 cm, we interpret the height as 7 cm (the edge perpendicular to the base). 5. **Volume formula for a pyramid:** $$V = \frac{1}{3} \times \text{Area}_{base} \times \text{height}$$ 6. **Calculate the volume:** $$V = \frac{1}{3} \times 12 \times 7 = 28 \text{ cm}^3$$ 7. **Final answer:** The volume of the triangular pyramid is **28 cubic centimeters**.