Question

a vertical pole of length 6M cast a shadow 4m long on the ground at the same time a tower cast a shadow 28 M long find the height of the tower

Answer 1

answer will be 84 m.
as thita will be same in both cases so in case 1 value of tan thita =6/2=3

in case 2
tan thita = height of tower /28
solve this by putting value of thita from case 1
height =84

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

PQ be vertical pole

Also,

PR be shadow

Also,

ST be vertical tower

So,

SN be it's shadow

Assume

ST = p metres

Hence,

In ∆PQR and ∆STN

∠P = ∠S = 90

Also,

∠R = ∠N

Hence,

By AA - criterion of similarity

∆PQR ~ ∆STN

${\boxed{\sf\:{\dfrac{PQ}{ST}=\dfrac{PR}{SN}}}}$

${\boxed{\sf\:{\dfrac{6}{p}=\dfrac{4}{28}}}}$

${\boxed{\sf\:{\dfrac{6}{p}=\dfrac{1}{7}}}}$

p = 6 × 7

p = 42

Therefore,

Height of tower = 42 m