1. **State the problem:** We need to find the volume of a right-angled triangular prism with a triangular base having sides 21 m and 37 m at a right angle, and the prism length (depth) is 15 m. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Area of base} \times \text{length}$$ 3. **Calculate the area of the triangular base:** Since the triangle is right-angled, the area is given by: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Here, base = 21 m and height = 37 m. 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 21 \times 37 = \frac{1}{2} \times 777 = 388.5 \text{ m}^2$$ 5. **Calculate the volume:** $$\text{Volume} = 388.5 \times 15 = 5827.5 \text{ m}^3$$ 6. **Final answer rounded to 1 decimal place:** $$\boxed{5827.5 \text{ m}^3}$$