The equation provided is:

$A = \frac{1}{2} h (b + c)$

We need to solve for $h$ in terms of $A$, $b$, and $c$. Let's go step by step:

1. Start by multiplying both sides of the equation by 2 to eliminate the fraction: $2A = h (b + c)$

2. Now, divide both sides by $(b + c)$ to solve for $h$: $h = \frac{2A}{b + c}$

So, the solution for $h$ is:

$h = \frac{2A}{b + c}$

Let me know if you need more details or further clarification!

Here are some related questions for you to consider:

1. How can this formula be used in real-world applications, such as calculating the height of a triangle?
2. What happens if $b + c = 0$? Is there any restriction for the variables?
3. Can you rearrange this formula to solve for $c$ instead?
4. How does this formula change if the $\frac{1}{2}$ is replaced by a different constant?
5. What is the significance of the term $b + c$ in this equation?

Tip: Always check if any variable in the denominator can make the expression undefined by becoming zero.