A) \[100\sqrt{3}\,\,\text{m}\]
B) \[50\sqrt{3}\,\,\text{m}\]
C) \[150\,\,\text{m}\]
D) \[\frac{150}{\sqrt{3}}\,\,\text{m}\]
Correct Answer: C
Solution :
Let height of the hill be h metre. |
In \[\Delta CDB,\] |
\[\tan 30{}^\circ =\frac{CD}{BD}\] |
\[\frac{1}{\sqrt{3}}=\frac{50}{BD}\] |
\[\Rightarrow \] \[BD=50\sqrt{3}\,\,\text{m}\] |
Again in \[\Delta ABD,\] |
\[\frac{AB}{BD}=\tan 60{}^\circ \] |
\[\Rightarrow \]\[\frac{AB}{50\sqrt{3}}=\sqrt{3}\] |
\[AB=50\sqrt{3}\times \sqrt{3}\]\[\Rightarrow \]\[h=150\,\,\text{m}\] |
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