Question : A person was standing on a road near a mall. He was 1425 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which was in between him and the mall, was exactly in the line of sight with the top of the mall. The tree's height is 10 m and it is 30 m away from him. How tall (in m) is the mall?
Option 1: 475
Option 2: 300
Option 3: 425
Option 4: 525
Correct Answer: 475
Solution :
Let, the height of the mall (AB) = $x$ m
From the figure,
CD = 10 m
DM = 30 m
BM = 1425 m
Let $\angle AMB = \angle CMD = \theta$
From $\triangle AMB$
$\tan \theta=\frac{\text{Perpendicular}}{\text{base}}=\frac{AB}{BM}$
From $\triangle CMD$,
$\tan \theta=\frac{\text{Perpendicular}}{\text{base}}=\frac{CD}{DM}$
⇒$\frac{AB}{BM}=\frac{CD}{DM}$
⇒ $\frac{x}{1425} = \frac{10}{30}$
⇒ $\frac{x}{1425} = \frac{1}{3}$
⇒ $x = 475$ m
Hence, the correct answer is 475 m.
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