A student bikes to school by traveling first d_N = 1.10 {miles} north, then d_W = 0.500 {miles} west, and finally d_S = 0.200 {miles} south. If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance d_b would the bird cover?

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To find the distance the bird would cover, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can consider the student's path as a right-angled triangle. The North-South path is the vertical side, the West-East path is the horizontal side, and the distance the bird would cover is the hypotenuse.

Let's calculate the distance using the Pythagorean theorem:

1. Calculate the square of the North-South distance (d_N^2):
d_N^2 = (1.10 miles)^2 = 1.21 miles^2

2. Calculate the square of the West-East distance (d_W^2):
d_W^2 = (0.500 miles)^2 = 0.25 miles^2

3. Add the squares of the two distances:
d_N^2 + d_W^2 = 1.21 miles^2 + 0.25 miles^2 = 1.46 miles^2

4. Take the square root of the sum to find the hypotenuse, which is the distance the bird would cover (d_b):
d_b = √(1.46 miles^2) ≈ 1.21 miles

Therefore, the bird would cover approximately 1.21 miles to travel directly from the origin to the school.