Question

.A person moves towards east for 3 m, then towards north for 4 m and then moves vertically up by 5 m. What is his distance now from the starting point?

Answer 1

Using the Pythagorean theorem, from the right triangle $\triangle AOB$ express $BO$.

$$BO = \sqrt{3^2 + 4^2} = 5$$

Using the Pythagorean theorem again, from the right triangle $\triangle BOC$ express $OC$, which is the final distance from the starting point.

$$OC = \sqrt{CB^2 + BO^2} = \sqrt{5^2 + 5^2} = 5\sqrt2$$

Answer. $5\sqrt2$.