A vertical pole of lenght 7.5m casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.
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Let AB be the vertical stick and let AC be its shadow.
Then, AB = 7.5m and AC = 5m
Let DE be the vertical tower and let DF be its shadow
Then, DF = 24m, Let DE = x meters
Now, In $\triangle\text{BAC}$ and $\triangle\text{EDF},$
$\triangle\text{BAC}\sim\triangle\text{EDF}$ by SAS criterion
$\Rightarrow\frac{\text{AB}}{\text{DE}}=\frac{\text{AC}}{\text{DF}}$
$\Rightarrow\frac{7.5}{\text{x}}=\frac{5}{24}$
$\Rightarrow\text{x}=\frac{7.5\times24}{5}=36\text{m}$
therefore, height of the vertical tower is 36m.
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