Final answer:
The length of the hypotenuse (side o) of the right-angled triangle can be found using the Pythagorean theorem, which gives us approximately 13.00 units when rounded to three significant figures.
Step-by-step explanation:
To find the length of the hypotenuse of a right-angled triangle when given the lengths of the other two sides, we use the Pythagorean theorem. The theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, if we assume that side m is one of the shorter sides and side n is the other, and we seek the length of the hypotenuse (side o), the Pythagorean theorem gives us:
o² = m² + n²
Plugging in the given values:
o² = (6.1 units)² + (11.48 units)²
o² = 37.21 units² + 131.8704 units²
o² = 169.0804 units²
Now, take the square root of both sides to find o:
o = √169.0804 units²
o ≈ 13.00 units (to three significant figures)