https://file.aiquickdraw.com/mathbot/file/1725415434121kcuj2nxs.jpg

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.

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

Learn how to calculate the height in a right triangle where AC = 18 and BC = 12 using the Pythagorean theorem and area formulas. Detailed step-by-step solution provided. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation