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Question
The length of DC is ______.
Options
10 m
\(10(\sqrt{3}+1) \mathrm{m}\)
20 m
\(10(\sqrt{3}-1) \mathrm{m}\)
MCQ
Fill in the Blanks
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Solution
The length of DC is \[\underline{\boldsymbol{10(\sqrt{3}-1) \mathrm{m}}}\].
Explanation:
We know that,
\[\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}\]
From figure,
In \[\triangle ABC,\]
\[\Rightarrow \tan 45^\circ = \frac{AB}{BC}\]
\[\Rightarrow 1 = \frac{10}{BC}\]
\[\Rightarrow BC = 10\ \text{m}.\]
In \[\triangle ABD,\]
\[\Rightarrow \tan 30^\circ = \frac{AB}{BD}\]
\[\Rightarrow \frac{1}{\sqrt{3}} = \frac{10}{BD}\]
\[\Rightarrow BD = 10\sqrt{3}\ \text{m}.\]
From figure,
\[DC = BD - BC = 10\sqrt{3} - 10 = 10(\sqrt{3} - 1)\ \text{m}.\]
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