Question

A hiker leaves camp and using a compass walks 3 km west then 4 km north. How far is the hiker from camp at this point and which direction should be taken to get back to camp?

Answer 1

Because the hiker walked directly west and then directly north the two legs of the hike forms a right triangle. Therefore we can use the Pythagorean Theorem to solve this problem.

The Pythagorean Theorem states:

`c^2 = a^2 + b^2`

Where:

`a` and `b` are legs of the triangle. In this case 3 km and 4 km.
`c` is the hypotenuse of the triangle which is what we are trying to solve for in this problem.

Substituting the values from the problem gives:

`c^2 = 3^2 + 4^2`

`c^2 = 9 + 16`

`c^2 = 25`

`sqrt(c^2) = sqrt(25)`

`c = 5`

The hiker is 5km from camp and should head in a generally south-east direction