A woman goes out running. She first travels 5.2km north. She then turns and travels 3.6km west. Finally, she turns If a bird were to start out from the origin (where the woman starts) and fly directly (in a straight line) to her final location, what distance d would the bird cover?again and travels 2.6km south. We are assuming a flat rectangular world.
as usual, draw a diagram. We want the diagonal of a right triangle with legs 3.6 and 5.2
so, the distance is √(3.6^2+(5.2-2.6)^2) = 4.4
To find the distance the bird would cover from the origin to the woman's final location, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 case, the woman's final location forms a right-angled triangle with sides 3.6 km and 2.6 km. We can use the Pythagorean theorem to find the length of the hypotenuse (which represents the distance the bird would cover):
d^2 = (3.6 km)^2 + (2.6 km)^2
Simplifying:
d^2 = 12.96 km^2 + 6.76 km^2
d^2 = 19.72 km^2
Taking the square root of both sides:
d ≈ 4.44 km
Therefore, the bird would cover approximately 4.44 km to fly directly from the origin to the woman's final location.