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.