# A hiker walks 12 miles due north. Then he turns and walks 16 miles due east. At this point, how many miles is the hiker from his starting point?

May 9, 2016

$20$ miles

#### Explanation:

Assuming the land is flat and the hiker is not close to one of the poles, he has traversed the two shorter sides of a right angled triangle, so we can use Pythagoras theorem to deduce the length of the hypotenuse:

$\sqrt{{12}^{2} + {16}^{2}} = \sqrt{144 + 256} = \sqrt{400} = 20$

This is a $3 , 4 , 5$ triangle scaled up by a factor of $4$ miles.