To solve the problem of finding the height of the triangular prism, let us break it down step by step:

Given:

• The length of the prism is $8 \, \text{m}$.
• The base of the triangular face is $7.2 \, \text{m}$.
• The volume of the prism is $144 \, \text{m}^3$.
• We are solving for the height of the triangular face.

Formula for the Volume of a Triangular Prism:

The volume $V$ of a triangular prism is calculated as: $V = \text{Base Area of the Triangle} \times \text{Length of the Prism}$

The area of the triangular face is: $\text{Base Area of the Triangle} = \frac{1}{2} \times \text{Base of the Triangle} \times \text{Height of the Triangle}$

Substitute this into the volume formula: $V = \frac{1}{2} \times \text{Base of the Triangle} \times \text{Height of the Triangle} \times \text{Length of the Prism}$

Substituting the Known Values:

We are given:

• $V = 144 \, \text{m}^3$
• Base of the triangle = $7.2 \, \text{m}$
• Length of the prism = $8 \, \text{m}$

Substitute into the formula: $144 = \frac{1}{2} \times 7.2 \times h \times 8$

Simplify step by step:

1. $\frac{1}{2} \times 7.2 = 3.6$
2. $3.6 \times 8 = 28.8$

So: $144 = 28.8 \times h$

Solve for $h$: $h = \frac{144}{28.8} = 5 \, \text{m}$

Final Answer:

The height of the triangular prism is: $\boxed{5 \, \text{m}}$

This matches the second option provided.

Do you need further details or clarifications?

Related Questions:

1. How is the formula for the volume of a triangular prism derived?
2. If the height of the triangle were doubled, what would the volume be?
3. What happens to the volume if the base of the triangular face is halved?
4. Can the same formula be used for other shapes of prisms? Why or why not?
5. What units are used to measure volume, and how do they differ from area or length?

Tip:

Always double-check whether the units are consistent across the problem (e.g., meters for length, cubic meters for volume) to avoid mistakes.