To solve for the height of the triangle, we use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}.$

Step 1: Substitute the given values

From the problem, we know: $\text{Area} = 24 \, \text{in}^2 \quad \text{and} \quad \text{base} = 8 \, \text{in}.$

Substitute into the formula: $24 = \frac{1}{2} \times 8 \times \text{height}.$

Step 2: Simplify the equation

First, simplify the multiplication: $24 = 4 \times \text{height}.$

Step 3: Solve for height

Divide both sides by 4: $\text{height} = \frac{24}{4} = 6 \, \text{in}.$

Final Answer:

The height of the triangle is: $\boxed{6 \, \text{in}}.$

Would you like further explanation or additional examples?

Here are 5 related questions to explore:

1. How do you find the height of a triangle if only its base and area are known?
2. What happens to the area if the height of the triangle doubles?
3. Can this method be applied to an isosceles triangle? Why or why not?
4. What is the formula for the area of other shapes, such as a trapezoid or parallelogram?
5. If the base changes to 10 inches and the area remains the same, how does the height change?

Tip: Always ensure the base and height are perpendicular to each other when calculating the area of a triangle.