Question

Девочка прошла от дома по направлению на запад 20м.Затем повернула на север и прошла 800м.После этого она повернула на восток и прошла еще 200м.На каком расстоянии(в метрах) от дома оказалась девочка?

Answer 1

Пусть дом - это точка А,
прошла на запад к точке В (АВ=20),
повернула на север к точке С (ВС=800),
повернула на восток к точке Д (СД=200)
Нужно найти расстояние АД.
Полученный четырехугольник АВСД - прямоугольная трапеция (АВ и СД - основания, <В=<С=90°). По т.Пифагора найдем АД:
АД²=ВС²+(СД-АВ)²=800²+(200-20)²=640000+32400=672400
АД=820 м

Answer 2

Answer in detail. The girl walked from home in the direction of the west 20m. Then she turned north and walked 800m. After that, she turned east and walked another 200m. How far (in meters) from home did the girl end up?

To answer this question, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance from the girl's home to her final position, and the other two sides are the horizontal and vertical displacements of the girl.

The horizontal displacement of the girl is the difference between the distance she walked west and the distance she walked east. Since she walked 20m west and 200m east, the horizontal displacement is 200m - 20m = 180m.

The vertical displacement of the girl is the distance she walked north, which is 800m.

Therefore, the distance from the girl's home to her final position is given by:

$$\sqrt{(180m)^2 + (800m)^2}$$

Using a calculator, we can find that this is approximately 815.4m. So, the girl ended up about 815.4m away from her home.