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At $4 : 00$ p.m. on a sunny day, a stick $2$ feet tall casts a shadow $5$ feet long. At the same time, a tree nearby casts a shadow $55$ feet long. What is the height in feet, of the tree ?

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137.5

27.5

22

10

answer is C.

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Detailed Solution

It is given the figure,
Question Image

Also given, stick height=

2

feet tall and stick shadow

= 5

feet long and at the same time, a tree nearby casts a shadow

55

feet long.
At the same time, the position of the sun will be fixed for both, hence the angle subtended by shadow on the tip of the tree will also be the same. Let the angle be

θ

Let

x

be the height of the tree in feet.
For stick, in

Δ A B C,

tan θ = P e r p e n d i c u l a r b a s e

tan θ = A B B C

tanθ = \frac{2}{5}

……..(1)
For tree, in

Δ D E F,

tan θ = P e r p e n d i c u l a r b a s e

tan θ = D E E F

tanθ = \frac{x}{55}

……..(2)
Equate (1) and (2), we get

\Rightarrow \frac{2}{5} = \frac{x}{55}

\Rightarrow x = \frac{2 \times 55}{5}

\Rightarrow x = 22

So the height of tree in feet is 22m.
So the correct option is 3.

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