To solve for the height $h$ in the formula for the area of a triangle, you start with the formula:

$A = \frac{1}{2} b h$

To solve for $h$, you can follow these steps:

1. Multiply both sides by 2 to get rid of the fraction: $2A = bh$

2. Divide both sides by $b$ to isolate $h$: $h = \frac{2A}{b}$

Now, you can substitute the given values into the equation to find the height:

• $A = 18 \, \text{in}^2$
• $b = 9 \, \text{in}$

$h = \frac{2 \times 18}{9} = \frac{36}{9} = 4 \, \text{in}$

So, the height $h$ of the triangle is 4 inches.

Would you like more details on this, or do you have any other questions?

Here are 5 related questions:

1. How would you solve for the base $b$ if you know the area $A$ and height $h$?
2. What is the formula for the area of a triangle if you know all three sides?
3. How would the formula change if you were calculating the area of a triangle using trigonometry?
4. What is the relationship between the area of a triangle and its perimeter?
5. How does the area formula change if you use different units for the base and height?

Tip: Always double-check the units of your measurements when calculating areas to ensure consistency and accuracy.