MCQ
In a right triangle $\text{ABC}, \angle\text{C}=90^\circ.$ If $\text{AC}=\sqrt3 BC$ and $ \angle\text{B}=\phi,$ then find its value.
- ✓$60^\circ$
- B$30^\circ$
- C$45^\circ$
- DNone of these
✓
Answer
Correct option: A.
$60^\circ$
Given : $\angle\text{C}=90^\circ.$
If $\text{AC}=\sqrt3 BC$ and $ \angle\text{B}=\phi,$
$\therefore\tan\phi=\frac{\text{AC}}{\text{BC}}$
$\Rightarrow\tan\phi=\frac{\sqrt3\text{BC}}{\text{BC}}=\sqrt3$
$\Rightarrow\tan\phi=\tan60^\circ\phi$
$\Rightarrow\phi=60^\circ$
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