https://file.aiquickdraw.com/mathbot/file/17268537863460wvfxizn.jpg

The problem shown in the image is written in Serbian and is about two right triangles \( \triangle ABC \). The task asks to calculate the sides of the shaded triangle that is similar to the given triangle.

Here’s the breakdown of the problem:
- The given right triangle \( \triangle ABC \) has sides labeled.
  - In the first triangle (left side of the image): \( AC = 6 \), \( BC = 8 \), and \( AB = 10 \), confirming it's a right triangle by the Pythagorean theorem (\(6^2 + 8^2 = 10^2\)).
  - There is a smaller shaded right triangle inside the first triangle, whose base and height are shown as 2 and 1, respectively.

- The second triangle on the right side shows a larger similar triangle, with \( AC = 8 \) and \( BC = 6 \), and its shaded part is a similar right triangle, also scaled accordingly.

The key point is that the problem asks to calculate the sides of the shaded triangle by using the property of similarity. Since the triangles are similar, the corresponding sides of the triangles will have the same ratio.

Shall I go ahead and calculate the sides of the shaded triangle using similarity properties, or do you need further clarification on some details first?

Based on the data from the image, calculate the sides of the shaded triangle that is similar to the given one. The triangles are right triangles with the first triangle having AC = 6, BC = 8, and AB = 10. The shaded triangle has a base of 2 and a height of 1 in the first diagram.

This problem involves calculating the sides of a shaded triangle similar to a given right triangle. The task covers concepts like similarity of triangles, proportionality, and the Pythagorean theorem. Suitable for students in Grades 8-10.

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