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.