Question

If $\sqrt{23}\sin x=\sqrt{17}$ and $\cos x>0$, what is the approximate value of $\tan x$?

• A. 1.28
• B. 1.35
• C. 1.68
• D. 1.79
• E. 2.03

Answer 1

The correct option is C 1.68

Given, $\sqrt{23}\sin x=\sqrt{17}$ and $\cos x>0$
$\Rightarrow \sin x=\frac{\sqrt{17}}{\sqrt{23}}$
$\Rightarrow \cos x=\sqrt{1-{\sin }^{2}x}=\sqrt{1-\frac{17}{23}}=\sqrt{\frac{6}{23}}$
Therefore $\tan x=\frac{\sin x}{\cos x}=\frac{\sqrt{17}}{\sqrt{6}}=1.68$