Question

A plane flies 320 km due west and then 240 km due north. Find the shortest

distance covered by the plane to reach its original position.​

Answer 1

The distance aeroplane needs to travel by the shortest distance is 400 km.

Answer 2

Given :

Plane flies 320 km due west and then 240 km due north

To Find :

The shortest  distance covered by the plane to reach its original position.​

Solution :

Let the starting point be A. The Plane flies from A to B covering 320 Km and then moves north and travels 240 km and reaches C.

Using Pythagoras Theorem we can find the shortest distance to reach the original position.

By Pythagoras Theorem,

         (Hypotenuse)² = (Base)² + (Perpendicular)²

or,            (AC)²           = (AB)²    +   (BC)²   (refer to the image attached)

or,            (AC)²           = (320)²  + (240)²

or,            (AC)²           = 102400 + 57600

or,            AC              = $\sqrt{160000}$

∴              AC              = 400 Km

∴  The shortest  distance covered by the plane to reach its original position. is 400 Km.