Question

Wesley sailed his boat due north for 18 miles, then due east for another 18 miles, approximately how far is Wesley from where he began?

Answer 1

Due north and due east have a 90 degree angle between them and they are both 18miles long so if we draw these two sides and join the start and finish ends of these two equal sides, we get a right angle triangle, with the one 90 degree angle and two 45 degree angles (by construction). Taking one 45 degree angle, and making the 18 miles the opposite side, and the hypotenuse or unknown long side as H then the cosine of the 45 degree angle is opposite/hypotenuse or O/H. So we say cos45=O/H and solving for H, then, H =O/cos45 = 18/071=25, so 25 is the answer.

Answer 2

Wesley is approximately 25 miles away from the place he started.


Say, Wesley started from point A, he rowed his boat in north direction, covered 18 miles and stopped at B. From B, he again rowed 18 miles towards east. Finally, he stopped at position C. 
From Pythagoras theorem, we can find, AC.

    AC² = AB² + BC²
⇒  AC² = 18² + 18²
⇒  AC² = 2×18² 
⇒  AC   = √2×18 ≈ 25 miles.