Question

a street light bulb is fixed on a pole 6 metre above the level of the street if a woman of height 1.5 metre Casts a shadow of 3 M find how far she is away from the base of the pole

Answer 1

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

Assumption

${\boxed{\sf\:{P\;be\;the\;position\;of\;street\:Bulb}}}$

PQ = 6m

RS = 1.5m

${\boxed{\sf\:{Height\;of\;woman\;and\;her\;shadow}}}$

TS = 3m

QS = p

Therefore,

SR || QP

∠S = ∠Q [90°]

∠R = ∠P [Corresponding ∠]

∠T = ∠T [Common]

$\tt{\rightarrow\triangle TSR\sim\triangle TQP(AA)}$

Therefore,

$\tt{\rightarrow\dfrac{TS}{TQ}=\dfrac{SR}{QP}=\dfrac{TR}{TP}}$

$\tt{\rightarrow\dfrac{3}{3+p}=\dfrac{1.5}{6}}$

18 = 4.5 + 1.5p

1.5p = 13.5

$\tt{\rightarrow p=\dfrac{13.5}{1.5}}$

= 9m

$\textsc{Distance\;of\;woman\;from\;base\;of\;the\;pole \;is\;9m}$