A) \[1:\sqrt{3}\]
B) \[2:3\]
C) \[\sqrt{3}:1\]
D) \[\sqrt{3}:\sqrt{2}\]
Correct Answer: C
Solution :
from figure \[\tan {{60}^{o}}=\frac{y}{x}\Rightarrow y=\sqrt{3}x\]?(i) \[\tan {{45}^{o}}=\frac{y}{x+BC}\] \[\Rightarrow \]\[x+BC=y=\sqrt{3}x\] \[\Rightarrow \]\[BC=\left( \sqrt{3}-1 \right)x\] ?(ii) \[\tan {{30}^{o}}=\frac{y}{x+CA}\] \[\Rightarrow \]\[x+CA=\sqrt{3}y=3x\]\[\Rightarrow \]\[CA=2x\] \[\Rightarrow \] ?..(iii) Hence \[AB:BC=\sqrt{3}\left( \sqrt{3}-1 \right)x:\left( \sqrt{3}-1 \right)x=\sqrt{3}:1\]You need to login to perform this action.
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