Question

A man goes 10 m due south and then 24 due west. How far is he from the starting point?

Answer 1

Let the man starts from point D and goes 10 m due south and stops at E. He then goes 24 m due west at F.
In right $△$DEF, we have:
DE = 10 m, EF = 24 m



$$\begin{gathered} D{F}^2=E{F}^2+D{E}^2 \\ DF=\sqrt{{10}^2+{24}^2} \\ =\sqrt{100+576} \\ =\sqrt{676} \\ =26\mathrm{m} \end{gathered}$$

Hence, the man is 26 m away from the starting point.