Question

an electric pole casts ashadow of length 20 m at a time. when a tree 6 m high casts a shadow of length 8 m. find the height of the pole

Answer 1

x:20::6:8
=>x×8=20×6
=>x=(20×6)÷8
=>x=120÷8
=>×=15

Answer 2

Hi !

Let PQ be the height of the pole .

In the figure ,

Height of tree = AB = 6m
Length of shadow of tree = BC =  8 m

Length of shadow of the pole = QR = 20 m

As both the objects cast shadow at the same time , the angle of elevation for both is same.

Hence , when drawn as a figure , both form two similar right triangles.

i.e.,

Δ ABC ~ Δ PQR

As they are similar , they must have sides proportional to each other ,

i.e.,

AB/PQ = BC/QR
6/PQ = 8/20

8PQ = 120

PQ =  15 m

Therefore,

Height of the pole is 15 m