Question

A man goes 15 m due west and then 8 m due north. How far is he from the starting point?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{O}\mathrm{be}\mathrm{the}\mathrm{starting}\mathrm{point}\mathrm{and}\mathrm{P}\mathrm{be}\mathrm{the}\mathrm{final}\mathrm{point}. \\ \mathrm{By}\mathrm{using}\mathrm{the}\mathrm{Pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{the}\mathrm{distance}\mathrm{OP}. \\ {15}^2+8^2={\mathrm{OP}}^2 \\ \Rightarrow {\mathrm{OP}}^2=225+64 \\ \Rightarrow {\mathrm{OP}}^2=289 \\ \Rightarrow \mathrm{OP}=17 \\ \mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{distance}\mathrm{is}17\mathrm{m}. \end{gathered}$$