Question

If $\theta$ is an acute angle for which ${\tan }^2\theta =6\tan \theta -9$, find the degree measure of $\theta$.

• A. $51.3$
• B. $60.0$
• C. $71.6$
• D. $79.7$
• E. $83.5$

Answer 1

The correct option is C $71.6$

Given, ${\tan }^2\theta =6\tan \theta -9$

$\Rightarrow {\tan }^2\theta -6\tan \theta +9=0$

$\Rightarrow {(\tan \theta -3)}^2=0$

$\Rightarrow \tan \theta -3=0$

$\Rightarrow \tan \theta =3$

But $\tan 71.6=3.0061$

Then $\theta ={71.6}^0$