A student bikes to school by traveling first d_N = 1.10 \rm {miles} north, then d_W = 0.500 \rm {miles} west, and finally d_S = 0.200 \rm {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?
1.17
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 length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, we can consider the north-south distance as the vertical side of the triangle and the west-east distance as the horizontal side of the triangle. The distance the bird would cover is the hypotenuse.
We can find the distance the bird would cover by using the formula:
d_b = √(d_N^2 + d_W^2)
where d_N is the north distance (1.10 miles) and d_W is the west distance (0.500 miles).
Plugging in the values, we have:
d_b = √(1.10^2 + 0.500^2)
Calculating the squares:
d_b = √(1.21 + 0.25)
Adding the values inside the square root:
d_b = √(1.46)
Taking the square root:
d_b ≈ 1.21 miles
Therefore, the bird would cover approximately 1.21 miles to travel directly from the origin to the school.