Question

bulb is 10m high on a pole. A man of height 2m is standing at a distance of 12m from the pole.
what is the length of his shadow?

Answer 1

Length of shadow is 3m

Answer 2

$Height \: of \:the \:pole (AB) = 10 \:m$

$Height \:of \: the \: man (CE) = 2\:m$

$Distance \:from \: man \:to \: foot \:of \\the \:pole (BC) = 12 \:m$

$Length \:of \:the \: shadow (CD) = x \:m$

$In \triangle DBA \: and \:\triangle DCE$

$\angle {ADB} = \angle {EDC} \: ( Common \:angle )$

$\angle {DBA} = \angle {EDC} = 90\degree$

$\therefore \triangle DBA \sim \triangle DCE$

$\blue {(A.A \: Property )}$

$\frac{AB}{DB} = \frac{EC}{DC}$

$\implies \frac{10}{x+12} = \frac{2}{x}$

$\implies 10x = 2(x+12)$

$\implies 10x = 2x + 24$

$\implies 10x - 2x = 24$

$\implies 8x = 24$

$\implies x = \frac{24}{8}$

$\implies x = 3$

Therefore.,

$\red{ Length \:of \:the \: shadow} \green {= 3\:m}$

•••♪