https://file.aiquickdraw.com/mathbot/file/1729539207071y81e51h0.jpg

The image presents two right-angled triangles, each with some given sides, and requires us to find the missing sides \(a\) and \(b\), rounded to 1 decimal place. We can use the Pythagorean theorem to find the lengths of these missing sides.

### 1st Triangle:
Given:
- One leg = 8 cm
- Another leg = 5 cm
- Hypotenuse = \(a\)

According to the Pythagorean theorem:

\[
a^2 = 8^2 + 5^2
\]
\[
a^2 = 64 + 25 = 89
\]
\[
a = \sqrt{89} \approx 9.4 \, \text{cm}
\]

### 2nd Triangle:
Given:
- Hypotenuse = 17 cm
- One leg = 12 cm
- Other leg = \(b\)

Applying the Pythagorean theorem again:

\[
17^2 = 12^2 + b^2
\]
\[
289 = 144 + b^2
\]
\[
b^2 = 289 - 144 = 145
\]
\[
b = \sqrt{145} \approx 12.0 \, \text{cm}
\]

### Final Answers:
- \(a \approx 9.4 \, \text{cm}\)
- \(b \approx 12.0 \, \text{cm}\)

Would you like further details or have any questions about these calculations?

### Related Questions:
1. How does the Pythagorean theorem apply to right-angled triangles?
2. What are the steps to calculate the hypotenuse in any right triangle?
3. Can you explain the difference between legs and hypotenuse in a triangle?
4. What are some common uses of the Pythagorean theorem in real life?
5. How do you find a missing leg if the hypotenuse is known?

### Tip:
Always double-check your units and rounding when solving geometric problems to ensure precision.

Work out the lengths of sides a and b. Give your answers to 1 decimal place. The given triangles have sides: 8 cm and 5 cm in one triangle, and 17 cm and 12 cm in the other.

Learn how to calculate the missing sides (a and b) of two right-angled triangles using the Pythagorean Theorem. Given sides are 8 cm, 5 cm for one triangle and 17 cm, 12 cm for the other. This solution is suitable for Grades 6-9 students.

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