The image contains a problem related to a triangle. Here is a transcription of the text:

"Given $AC = 18$ and $BC = 12$, find the height $h$ from $B$ to $AC$."

The problem provides the lengths of the sides $AC$ and $BC$ of a triangle and asks for the height $h$ from point $B$ perpendicular to side $AC$.

Let's proceed with solving this problem.

Solution:

To find the height $h$, we can use the Pythagorean theorem. Assuming that $\triangle ABC$ is a right triangle with $\angle ABC = 90^\circ$:

1. Use the Pythagorean theorem: $AB^2 = AC^2 + BC^2$ Substitute the given values: $AB^2 = 18^2 + 12^2 = 324 + 144 = 468$ $AB = \sqrt{468} = \sqrt{4 \times 117} = 2\sqrt{117} \approx 21.63$

2. Find the area using base $AC$ and height $h$: The area $A$ of $\triangle ABC$ can also be expressed as: $A = \frac{1}{2} \times AC \times h$

3. Find the area using base $BC$ and height $AB$: Another way to express the area is: $A = \frac{1}{2} \times BC \times AB$ Substituting the known values: $A = \frac{1}{2} \times 12 \times 21.63 \approx 129.78$

4. Equating both expressions for the area: $\frac{1}{2} \times 18 \times h = 129.78$ Solving for $h$: $h = \frac{129.78 \times 2}{18} \approx \frac{259.56}{18} \approx 14.42$

So, the height $h$ from point $B$ to line $AC$ is approximately 14.42 units.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you calculate the area of a triangle using other side lengths?
2. What other methods can be used to find the height in non-right triangles?
3. What is the importance of understanding the properties of right triangles in trigonometry?
4. How does the Pythagorean theorem apply to triangles that are not right-angled?
5. Can we use trigonometric ratios to find the height in this case? If so, how?

Tip: When dealing with triangles, always consider the possibility of using trigonometric identities or properties such as the Pythagorean theorem to simplify the calculations.