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The problem presents a right triangle with \( R \) as the hypotenuse, \( x = 6 \, \text{m} \) as the base, and \( y = 8.2 \, \text{m} \) as the height. To find the magnitude of \( R \), we can use the Pythagorean theorem:

\[
R = \sqrt{x^2 + y^2}
\]

Now, substituting the values:

\[
R = \sqrt{(6 \, \text{m})^2 + (8.2 \, \text{m})^2}
\]

Let me calculate that for you.The magnitude of \( R \) is approximately \( 10.16 \, \text{m} \).

Would you like further details or explanations? Here are some related questions:

1. How can the Pythagorean theorem be used in different types of problems?
2. What are the practical applications of this theorem in real-life scenarios?
3. Can you find the angles of this triangle using trigonometry?
4. How would you solve the problem if the hypotenuse \( R \) and one side were given instead?
5. How do units affect the accuracy and precision of measurements?

**Tip:** Always make sure to use consistent units when solving problems involving measurements.

Solve for the magnitude of R if x is 6 m and y is 8.2 m.

Learn how to solve for the hypotenuse of a right triangle using the Pythagorean theorem. Given x = 6 m and y = 8.2 m, we calculate the magnitude of R. Suitable for students in Grades 7-10.

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