To apply the Pythagorean Theorem, we need to treat the numbers provided as coordinates in a 2D space. Generally, the theorem is expressed as:
\[ c = \sqrt{a^2 + b^2} \]
Where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides of a right triangle formed by the two points.
To proceed, let's assume that the numbers you provided represent the coordinates of two points as follows:
- Point A: (6.40, 5.57)
- Point B: (41, 9)
Now, we will calculate the length between these two points \(A\) and \(B\). We can find the differences in the coordinates:
\[ \Delta x = x_2 - x_1 = 41 - 6.40 = 34.60 \] \[ \Delta y = y_2 - y_1 = 9 - 5.57 = 3.43 \]
Now we can use these differences in the Pythagorean Theorem:
\[ c = \sqrt{(34.60)^2 + (3.43)^2} \]
Calculating the squares:
\[ (34.60)^2 = 1197.16 \] \[ (3.43)^2 = 11.7649 \]
Adding these squares:
\[ 1197.16 + 11.7649 = 1208.9249 \]
Now, we take the square root:
\[ c = \sqrt{1208.9249} \approx 34.77 \]
Rounding to the nearest hundredth, the length between the two points is approximately:
\[ \boxed{34.77} \]
1 answer