An airplane flies 400 km west from city A to city B, then 200km northwest to city c and finally 100 km north to city D. How far it is from city a to d?
D = -400 + 200[135o] + 100i = -400 - 141.4+141.4i + 100i = -541.4 + 241.4i = 593 km[24o] N. of W.
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To find the distance from City A to City D, you can use the Pythagorean theorem, which states that in a right-angled 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, the triangle formed by City A, City B, and City C is a right-angled triangle. The distance from City A to City B (400 km) is the base of the triangle, and the distance from City B to City C (200 km) is the perpendicular side.
Using the Pythagorean theorem, we can calculate the hypotenuse, which is the distance from City A to City C:
Hypotenuse^2 = Base^2 + Perpendicular^2
Distance from A to C^2 = 400^2 + 200^2
Distance from A to C = √(400^2 + 200^2) = 447.21 km (approximately)
Now, to find the distance from City A to City D, we need to consider the triangle formed by City A, City C, and City D. The distance from City A to City C (447.21 km) is the base of this triangle, and the distance from City C to City D (100 km) is the perpendicular side.
Using the Pythagorean theorem again, we can calculate the hypotenuse, which is the distance from City A to City D:
Hypotenuse^2 = Base^2 + Perpendicular^2
Distance from A to D^2 = 447.21^2 + 100^2
Distance from A to D = √(447.21^2 + 100^2) = 459.55 km (approximately)
Therefore, the distance from City A to City D is approximately 459.55 km.