To solve for $c$, the hypotenuse, using the Pythagorean theorem $a^2 + b^2 = c^2$, let’s substitute the values:

Given:

• $a = 4.1 \, \text{m}$
• $b = 6.6 \, \text{m}$

1. Square the sides: $a^2 = (4.1)^2 = 16.81$ $b^2 = (6.6)^2 = 43.56$

2. Add the squares: $a^2 + b^2 = 16.81 + 43.56 = 60.37$

3. Take the square root to find $c$: $c = \sqrt{60.37} \approx 7.8$

Final Answer:

The hypotenuse $c$ is approximately 7.8 meters.

Does this explanation help? Let me know if you need further clarification!

Here are 5 related questions to expand your understanding:

1. How do you determine the hypotenuse for any right triangle?
2. If one side is unknown, how can you solve for it using the Pythagorean theorem?
3. What are real-life examples where the Pythagorean theorem is used?
4. How do you verify if a triangle is a right triangle using side lengths?
5. How do you solve a triangle problem with decimals or fractions?

Tip: Always square the values carefully to avoid rounding errors when using the Pythagorean theorem!