sin x=5/13 tan x=-5/12 ;x=?![]()
You're looking for an angle whose terminal side is in the second quadrant, since that's the quadrant where Sin is positive and Tan is negative.
$\displaystyle \theta=\arcsin\left(\frac{5}{13}\right)\approx22.6 ^\circ$
The reference angle in the 2nd quadrant is $\displaystyle 22.6^\circ$
For any angle $\displaystyle \theta, \ \ 0 < \theta < 180^\circ$, its reference angle is defined as $\displaystyle 180^\circ - \theta$
$\displaystyle \theta = 180^\circ - 22.6^\circ \approx 157.4^\circ$