W m straight west and then N m straight north

Problem:

Suppose you walk W m straight west and then N m straight north. How far are you from your starting point?

Solution:

If you walk W m straight west and then N m straight north, you will form a right triangle with legs W m and N m. The hypotenuse of this triangle is the distance you are from your starting point.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the distance you are from your starting point is:

d² = W² + N²

where:

• d is the distance from your starting point (in meters)
• W is the distance you walked west (in meters)
• N is the distance you walked north (in meters)

Taking the square root of both sides, we get:

d = √(W² + N²)

This is the formula for calculating the distance you are from your starting point.

For example, if you walk 10 m west and 20 m north, then the distance you are from your starting point is:

d = √(10² + 20²) = √(100 + 400) = √500 = 22.36 m

Therefore, you are 22.36 m from your starting point.