The problem requires using the Pythagorean theorem to find the missing side in both right triangles.

The Pythagorean theorem states that for a right-angled triangle:

$a^2 + b^2 = c^2$

Where:

• $c$ is the hypotenuse (the longest side),
• $a$ and $b$ are the other two sides.

a) Triangle with sides 6 and 3:

We are missing the hypotenuse ($c$).

$c^2 = 6^2 + 3^2 = 36 + 9 = 45$ $c = \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \approx 6.71$ Thus, the hypotenuse is approximately $6.71$.

b) Triangle with sides 7.4 and 3.6:

We are again missing the hypotenuse ($c$).

$c^2 = 7.4^2 + 3.6^2 = 54.76 + 12.96 = 67.72$ $c = \sqrt{67.72} \approx 8.23$ Thus, the hypotenuse is approximately $8.23$.

Would you like further details on any part of the calculation?

Here are 5 questions to expand your understanding:

1. How can you apply the Pythagorean theorem to determine the missing side when the hypotenuse is known?
2. What are some real-life applications of the Pythagorean theorem?
3. How would the result change if one of the side lengths in either triangle was doubled?
4. What is the significance of the square root operation in the Pythagorean theorem?
5. How would you solve the problem if the triangle were not a right-angled triangle?

Tip: Always ensure that the longest side is used as the hypotenuse in the Pythagorean theorem.