If a vertical stick 12 m long casts a shadow 8 m long on the ground and at the same time a tower casts a shadow 40 m long on the ground, then the height of the tower is

Let AB be the stick of length 12 m and BC be the shadow 8 m long. Similarly DE be the tower with shadow 40 m long.

In ΔABC and ΔDEF,

∠ ABC =∠ DEF {90° each}

∠ BCA = ∠ EFD {angular elevation is same at the same instant}

By the criterion of similar triangle AA which says that

if two angles of one triangle are respectively equal to two angles of another triangle then the two triangles are similar

ΔABC ~ ΔDEF

{Corresponding sides of the similar triangles are in same ratio}