Question

a runaway prisoner first goes 1.70 km directly to the east from the prison, and then he goes straight to the north to reach his hideout. if the total distance he moves is 2.50 km, what direction is he from the east?

Answer 1

The prisoner is 39° north of west from the east after traveling 1.70 km east and then approximately 1.38 km north to reach a total distance of 2.50 km.

Step-by-step explanation:

The prisoner first travels 1.70 km east and then moves in a straight line north to reach a total distance of 2.50 km. We can use Pythagorean theorem (a^2 + b^2 = c^2) to find the northward distance which comes out to be approximately 1.38 km. Thus, from the east, he is approximately north 39° west.

Pythagorean theorem is used because we're dealing with a right triangle when the prisoner moves first east and then north. The direct distance from the prison to the hideout is the hypotenuse of the right triangle.

The northward direction is computed as the inverse tangent of the upward travel (approximately 1.38 km) over the eastward travel (1.70 km), which results in an angle nearly 39° north of west.

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