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

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

where:

• $A$ is the area of the triangle,
• $b$ is the base of the triangle, and
• $h$ is the height of the triangle.

Steps to solve for $h$:

1. Multiply both sides by 2 to eliminate the fraction: $2A = b h$

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

Thus, the formula for $h$ in terms of $A$ and $b$ is:

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

This formula allows you to calculate the height of a triangle if you know its area and base.

Would you like further details or have any questions?

Here are some related questions that build on this topic:

1. How can you calculate the area if you know the base and height of a triangle?
2. What happens to the height if the area doubles while the base stays the same?
3. Can the base or height be negative in the context of calculating area?
4. How does the formula change for other types of triangles (e.g., equilateral)?
5. How can you verify if a triangle is right-angled given the base, height, and hypotenuse?

Tip: For a triangle, always ensure that the base and height are perpendicular to each other.