If you travel 15 mi east and then 10 mi north, how far are you from your starting point?. Give the solution and explain it.

Question

sburchette · Answer

This simply forms a right triangle with legs of length 15 and 10.  Your distance from the starting point will be the hypotenuse that the triangle forms.  You can use the Pythagorean Theorem to find the length of the hypotenuse.  The theorem states, $$a^2+b^2=c^2$$Where a and b are the length of the legs. So solving for c (and ignoring the negative value that taking the square root produces because we are discussing lengths) you get$$c=\sqrt{a^2+b^2}$$You can substitute 15 and 10 into the equation for a and be and you get$$c=\sqrt{10^2+15^2}$$Which reduces to $$c=\sqrt{325}\approx18.03$$ so you are about 18 miles from your starting point.