$A$ flag pole $18 \, m$ high casts a shadow $9.6 \, m$ long. Find the distance of the top of the pole from the far end of the shadow. (in $m$)

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $m \angle A = 60^{\circ}$. If $AC = 10$,then $AB = \dots$

If $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$,and $\frac{AB}{4} = \frac{XY}{5}$,then $\frac{BC}{YZ} = \ldots$

It is given that $\triangle ABC \sim \triangle EDF$ such that $AB = 5 \, cm$,$AC = 7 \, cm$,$DF = 15 \, cm$,and $DE = 12 \, cm$. Find the lengths of the remaining sides of the triangles.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $\frac{AM}{MB} = \frac{4}{5}$ and $NC = 2.5$,find $AN$.

Prove that the sum of squares of the sides of a rectangle is equal to the sum of squares of its diagonals.