MCQ
In a right triangle $\text{ABC}, \angle\text{C}=90^\circ.$ If $ \text{AC}=\sqrt{3} BC$ and $ \angle\text{B}=\text{f},$ then find its value.
- A$45^\circ$
- B$30^\circ$
- ✓$60^\circ$
- DNone o these
✓
Answer
Correct option: C.
$60^\circ$
Given : $\angle\text{C}=90^\circ.$ If $ \text{AC}=\sqrt{3} BC$ and $\angle\text{B}=\phi$
$\therefore\tan\phi=\frac{\text{AB}}{\text{BC}}$
$\Rightarrow\tan\phi=\frac{\sqrt{3}\text{BC}}{\text{BC}}=\sqrt{3}$
$\Rightarrow\tan\phi=\tan60^\circ\phi$
$\Rightarrow\phi=60^\circ$
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