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Question

Answers

A) $7m$

B) \[3.5m\]

C) \[5m\]\[\]

D) \[14m\]

Answer
Verified

First, we draw the figure with given data.

Here \[AB\text{ }=~7m\](height of tree)

Angle \[C\text{ }={{45}^{0}}\](angle of elevation) A

We need to find \[BC\] (length of shadow)

\[D\] = Point of elevation (Sun)

\[{{45}^{0}}\]

Here \[AB\] can be considered as perpendicular to the Right triangle ABC and \[BC\] can be the base of the triangle ABC.

Hence the required ratio is \[tan\]and angle is \[{{45}^{0}}\].

So, \[\tan \theta =\dfrac{perpendicular}{base}=\dfrac{AB}{BC}\]

Put known values,

\[\Rightarrow \tan {{45}^{0}}=\dfrac{7m}{BC}\]

As we know that, $\tan 45{}^\circ =1$

\[\Rightarrow 1=\dfrac{7m}{BC}\]

Applying cross multiplication:

\[1\times BC=7m\]

The length of the shadow of a tree$7m$high, when the sunâ€™s elevation is\[{{45}^{0}}\], is $=7m$

Hence, from the given multiple options, option A is the correct answer.