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?

1 Answer
smendyka
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

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