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A vertical stick 12 m long …

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A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Determine the height of tower.
  • 1 answers

Sia ? 6 years, 6 months ago

Let AB be the vertical stick and AC be its shadow. Also, let DE be the vertical tower and DF be its shadow. Join BC and EF. Let DE = x metres.
We have,
AB = 12 m, AC = 8m, and DF = 40m.
In {tex}\Delta{/tex} ABC and {tex}\Delta{/tex}DEF, we have,
{tex}\angle{/tex}A = {tex}\angle{/tex}D = 90° and {tex}\angle{/tex}C = {tex}\angle{/tex}F [Angular elevation of the sun]
Therefore, by AA- criterion of similarity, we obtain {tex}\Delta A B C \sim \Delta D E F{/tex}

{tex}\Rightarrow \quad \frac { A B } { D E } = \frac { A C } { D F }{/tex}
{tex}\Rightarrow \quad \frac { 12 } { x } = \frac { 8 } { 40 } \Rightarrow \frac { 12 } { x } = \frac { 1 } { 5 } \Rightarrow x {/tex} = 60 metres

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