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The image contains a math problem related to right triangles and the Pythagorean theorem. Here is a translation and breakdown of the problem:

**Problem 5:** Determine the unknown side lengths of each triangle.

### a. Given a right triangle \(\triangle ABC\) with:
- \( \angle A = 90^\circ \)
- \( BC = 26 \, \text{cm} \)
- \( AB = 10 \, \text{cm} \)

Find \( AC \).

### Solution for a:

Using the Pythagorean theorem for a right triangle:
\[
AC^2 = BC^2 - AB^2
\]

\[
AC^2 = 26^2 - 10^2
\]

\[
AC^2 = 676 - 100 = 576
\]

\[
AC = \sqrt{576} = 24 \, \text{cm}
\]

### b. Given a right triangle \(\triangle ABC\) with:
- \( \angle B = 90^\circ \)
- \( AC = 15.3 \, \text{cm} \)
- \( AB = 10.2 \, \text{cm} \)

Find \( BC \).

### Solution for b:

Using the Pythagorean theorem:
\[
BC^2 = AC^2 + AB^2
\]

\[
BC^2 = 15.3^2 + 10.2^2
\]

\[
BC^2 = 234.09 + 104.04 = 338.13
\]

\[
BC = \sqrt{338.13} \approx 18.4 \, \text{cm}
\]

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### Related Questions:
1. How do you apply the Pythagorean theorem to non-right triangles?
2. What are the conditions under which the Pythagorean theorem can be used?
3. How do you calculate the perimeter of a triangle once all sides are known?
4. What is the relationship between trigonometric ratios and the sides of a right triangle?
5. How do you solve problems involving special right triangles (30-60-90, 45-45-90)?

**Tip:** Always double-check your calculations when applying the Pythagorean theorem, especially when dealing with decimals or square roots.

Tentukan ukuran sisi yang belum diketahui dari setiap segitiga berikut.
a. Diketahui ΔABC dengan ∠A = 90°, BC = 26 cm, dan AB = 10 cm.
b. Diketahui ΔABC dengan ukuran AB = 10,2 cm, AC = 15,3 cm, dan ∠B = 90°.

Learn how to find the missing side lengths of right triangles using the Pythagorean theorem. This example includes two problems involving triangles with given side lengths and right angles. Suitable for students in Grades 8-10.

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