To find the volume of the triangular prism, you need to use the formula for the volume of a prism:

$V = \text{Area of the base} \times \text{Height}$

Here, the base is a right triangle, and the height is given as 10 inches. The right triangle has legs of 9 inches and 8 inches.

1. First, find the area of the right triangle base using the formula for the area of a right triangle:

$\text{Area of base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 8 = 36 \, \text{square inches}$

2. Then, multiply the area of the base by the height (10 inches) of the prism:

$V = 36 \times 10 = 360 \, \text{cubic inches}$

Thus, the volume of the triangular prism is 360 cubic inches.

Would you like more details or have any questions about the solution?

Here are five related questions you might find helpful:

1. How do you calculate the area of a right triangle?
2. What other types of prisms are there, and how do their volumes differ?
3. How would the volume change if the height of the prism were increased?
4. What is the formula for the volume of a rectangular prism?
5. How do you find the volume of a prism when the base is not a triangle?

Tip: Remember to always ensure you are using the correct measurements for base, height, and prism height when calculating volumes.