In a triangle ABC, AB = 17 cm, BC = 12 cm and ∠ ABC = 90°. Determine the length of AC.

145 space c m

12.04 space c m

20.81 space c m

433 space c m

To find the length of side \( AC \) in the right triangle \( ABC \), where \( \angle ABC = 90^\circ \), we can use the Pythagorean theorem. The theorem states:

\[
AC^2 = AB^2 + BC^2
\]

Given:
- \( AB = 17 \) cm
- \( BC = 12 \) cm

Substitute the values into the Pythagorean theorem:

\[
AC^2 = 17^2 + 12^2
\]

\[
AC^2 = 289 + 144
\]

\[
AC^2 = 433
\]

To find \( AC \), take the square root of 433:

\[
AC = \sqrt{433} \approx 20.81 \, \text{cm}
\]

So, the correct answer is \( \textbf{20.81 cm} \).

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Do you want more details, or have any questions?

Here are 5 related questions to consider:
1. How would you calculate the area of triangle ABC?
2. If the length of AC was known, how could you find the other sides?
3. Can the Pythagorean theorem be applied to any triangle?
4. How does the Pythagorean theorem relate to the distance formula in coordinate geometry?
5. What are the properties of a 45°-45°-90° triangle?

**Tip:** The Pythagorean theorem is only applicable in right-angled triangles.

Learn how to determine the length of side AC in triangle ABC with a detailed step-by-step solution using the Pythagorean theorem. Given sides AB = 17 cm and BC = 12 cm, calculate AC. Suitable for students in Grades 7-9.

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