Question

A man goes 35 m due west and then 12 m due north. How far is he from the starting point?

Answer 1

Suppose the man starts at point A and goes 35 m towards west, say AB. He then goes 12 m north, say BC.



We need to find AC.

By Pythagoras theorem:
${\mathrm{AC}}^2={\mathrm{BC}}^2+{\mathrm{AB}}^2$
$$\begin{gathered} \Rightarrow {\mathrm{AC}}^2={35}^2+{12}^2 \\ \Rightarrow {\mathrm{AC}}^2=1225+144 \\ \Rightarrow {\mathrm{AC}}^2=1369 \\ \Rightarrow {\mathrm{AC}}^2={37}^2 \\ \Rightarrow \mathrm{AC}=37\mathrm{m} \end{gathered}$$

Hence, the man is 37 m far from the starting point.