[Math] The obtuse angle $B$ is such that $\tan B = -\frac{5}{12}$. Find the exact value of $\sin B$.

trigonometry

The obtuse angle $B$ is such that $\tan B = -\frac{5}{12}$. Find the exact value of $\sin B$.

Is this possible to do without a calculator? If so, how?

Best Answer

Notice, the obtuse angle $B$ ($90^\circ<B<180^\circ$) lies in second quadrant hence the value of $\sin B$ is positive & is given as follows in terms of $\tan B$,
$$\sin B=\left|\frac{\tan B}{\sqrt{1+\tan^2 B}}\right|=\left|\frac{\frac{-5}{12}}{\sqrt{1+\left(\frac{-5}{12}\right)^2}}\right|=\frac{5}{13}$$

Related Question