The boy walked 550 m from the house towards the east. Then he turned north and walked 480 m.

The boy walked 550 m from the house towards the east. Then he turned north and walked 480 m. How far from the house was the boy?

1. Since the boy first moved to the east, and then turned to the north, it means that he turned at an angle of 90 degrees.
2. Consequently, the boy’s trajectory had the following shape – _l. To find the distance at which he moved away from the house, it is necessary to draw a straight line from the point corresponding to the beginning of the movement to the point corresponding to its end. The desired distance is the hypotenuse of a triangle with sides 550 m and 480 m.
By the Pythagorean theorem:
√ (550 ^ 2 + 480 ^ 2) = 10 * √ (55 ^ 2 + 48 ^ 2) = 10 * √ (3025 + 2304) = 10 * √5329 = 10 * 73 = 730.
Answer: 730 m.