https://file.aiquickdraw.com/mathbot/file/1726740731408lb88f4sc.jpg

The diagram you've provided shows a triangle with:

- \( AB = 152 \, \text{cm} \)
- \( BC = 3000 \, \text{cm} \)
- The angle \( \angle ACB = 26.927^\circ \)

To find \( h \) (height), which is represented by the vertical distance from point \( D \) to point \( B \), we can use trigonometry based on the right triangle formed by points \( A \), \( B \), and \( C \).

### Using the angle \( \angle ACB = 26.927^\circ \) and the known base \( BC = 3000 \, \text{cm} \), we can use the tangent function:
\[
\tan(\theta) = \frac{h}{BC}
\]

Here, \( \theta = 26.927^\circ \) and \( BC = 3000 \, \text{cm} \), so:
\[
\tan(26.927^\circ) = \frac{h}{3000}
\]

Now, we calculate \( h \).

Let me compute this for you.The height \( h \), which is the vertical distance from point \( D \) to point \( B \), is approximately \( 1523.76 \, \text{cm} \).

Would you like more details or have any other questions?

Here are five related questions for further exploration:
1. How would the height \( h \) change if the angle \( \angle ACB \) increased?
2. Can we calculate the length of side \( AB \) using this information?
3. How do we compute the area of this triangle using the given data?
4. What would happen to the height if the length of \( BC \) were reduced by half?
5. How can we find the distance from point \( D \) to \( C \)?

**Tip**: In right triangles, trigonometric functions like sine, cosine, and tangent are key tools for determining unknown lengths and angles when certain values are provided.

Find h based on the triangle with AB = 152 cm, BC = 3000 cm, and angle ∠ACB = 26.927°.

Learn how to find the height of a right triangle given AB = 152 cm, BC = 3000 cm, and angle ∠ACB = 26.927°. Using trigonometry, this problem demonstrates how to apply the tangent function to calculate the height. Suitable for high school students in Grades 9-12.

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