# 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?

Feb 2, 2017

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