Question

A flagpost casts a 16.8m shadow. At the same time 2.4m shadow is cast by a person who is 1.8m tall. Find the height of the flagpost.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}\angle \mathrm{ACB}=\angle \mathrm{DFE}(\because \mathrm{Angle}\mathrm{of}\mathrm{elevation}\mathrm{of}\mathrm{the}\mathrm{Sun}\mathrm{at}\mathrm{the}\mathrm{same}\mathrm{time}) \\ \mathrm{In}△\mathrm{ABC}\mathrm{and}△\mathrm{DEF},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{ABC}=\angle \mathrm{DEF}=90°\left(\mathrm{Given}\right) \\ \angle \mathrm{ACB}=\angle \mathrm{DFE}\left(\mathrm{Given}\right) \\ \therefore △\mathrm{ABC}\cong △\mathrm{DEF}(\mathrm{AA}\mathrm{test}) \\ \mathrm{Then}\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}} \\ \Rightarrow \frac{\mathrm{AB}}{1.8}=\frac{16.8}{2.4} \\ \Rightarrow \mathrm{AB}=12.6\mathrm{m} \end{gathered}$$