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?

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?

Julia Adams · Accepted Answer

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

Ethan Adkins · Answer

undefined The hiker is 5 km away from camp at this point. To get back to camp, the hiker should take the opposite direction of the path taken. In this case, the hiker should walk 4 km south and then 3 km east.