A 15 high tower casts a sshadow 24 long at a certain time at the same time, a telephone pole casts a shadow 16 long. Find the height of the telephone pole.

Explanation

Let BC=15 m be the tower and its shadow AB is 24 m. At that time `angleCAB=theta`. Again, let EF=h be a telephone pole and its shadow DE= 16 m. At the same time `angleEDF=theta`.
Here , `DeltaABC and DeltaDEF ` both are right angled triangles.

In `DeltaABC and Delta DEF angleCAB=angleEDF=theta`
`angleB=angleE` [each `90^(@)`]
`DeltaABC~DeltaDEF` [by AAA similarity creterion]
Then, `(AB)/(DE)=(BC)/(EF)`
`rArr 24/16=15/h`
`therefore h=(15xx16)/24=10`
Hence, the height of the telephone pole is 10 m.