A) \[\frac{20}{\sqrt{3}}(\sqrt{3}-1)\]
B) \[\frac{20}{\sqrt{3}}(\sqrt{3}+1)\]
C) \[20\sqrt{3}\]
D) \[\frac{20}{\sqrt{3}}\]
Correct Answer: B
Solution :
Let SP and RQ be two pillars in |
which SP = 20 m |
Here, |
Let \[ST\bot RQ\] |
Then, \[\angle RST=30{}^\circ \] and |
Let \[RT=x,\]\[SP=TQ=20\,\,\text{m}\] |
Also, SP = PQ |
As \[\theta =45{}^\circ \]\[\Rightarrow \]\[PQ=ST=20\,\,\text{m}\] |
In \[\Delta SRT,\]\[\tan 30{}^\circ =\frac{x}{ST},\]\[\frac{x}{20}=\frac{1}{\sqrt{3}}\]\[\Rightarrow \]\[x=\frac{20}{\sqrt{3}}\] |
\[\therefore \]Height of pillar \[RQ=RT+TQ\] |
\[=20+\frac{20}{\sqrt{3}}=\frac{20\,\,(\sqrt{3}+1)}{\sqrt{3}}\] |
You need to login to perform this action.
You will be redirected in
3 sec