Question

If $cosec\theta =1.66$, then $\tan \theta$ equals:

• A. 0.6
• B. 0.76
• C. 1.32
• D. 1.76

Answer 1

The correct option is B 0.76

Given that $cosec\theta =1.66$

$\Rightarrow cosec\theta =\frac{166}{100}=\frac{83}{50}$

We know that $cosec\theta =\frac{hypotenuse}{perpendicular}$

Then right angle triangle hypotenuse=83 and perpendicular 50

Then, base $=$ $\sqrt{(83{)}^2-(50{)}^2}=\sqrt{6889-2500}=\sqrt{4389}=66.25$

But $\tan \theta =\frac{hypotenuse}{base}=\frac{50}{66.25}=0.7549$

Then $\tan \theta =0.76$