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The image you've uploaded shows a right triangle with two smaller triangles inside it, where the larger triangle has a height of \(2h\) and the smaller triangle has a height of \(h\). The angle at the top of the smaller triangle is \(22^\circ\).

To solve for various aspects of this triangle, let's first identify what we can find:

1. **Finding the base of the smaller triangle:**
   Since we have the height \(h\) and the angle \(22^\circ\), we can use the tangent function:

   \[
   \tan(22^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\text{base}}
   \]
   \[
   \text{base} = \frac{h}{\tan(22^\circ)}
   \]

2. **Finding the base of the larger triangle:**
   Similarly, for the larger triangle with height \(2h\), we use the same angle:

   \[
   \tan(22^\circ) = \frac{2h}{\text{base (larger triangle)}}
   \]
   \[
   \text{base (larger triangle)} = \frac{2h}{\tan(22^\circ)}
   \]

3. **Difference in the bases** will give us the length of the remaining segment of the base of the right triangle.

Would you like to proceed with these calculations, or is there a specific part of the problem you are interested in exploring further? 

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**Relative Questions:**

1. How would the problem change if the angle was different from \(22^\circ\)?
2. Can we find the hypotenuse of the triangles using the given information?
3. What if the height of the larger triangle was not exactly twice that of the smaller one? How would the calculations change?
4. How does knowing just one angle and a side help in determining the dimensions of a triangle?
5. How can trigonometric identities assist in solving problems involving right triangles?

**Tip:** In trigonometry, always make sure you correctly identify which side corresponds to the angle you're using—opposite, adjacent, or hypotenuse—to avoid calculation errors.

Given a right triangle with two smaller triangles inside it, where the larger triangle has a height of 2h and the smaller triangle has a height of h. The angle at the top of the smaller triangle is 22°. Solve for various aspects of this triangle.

Explore how to solve a right triangle problem involving an angle of 22 degrees and different heights of h and 2h. Learn how to apply the tangent function to find the base of each triangle. Suitable for students in Grades 10-12.

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