In such type of questions, it is mentioned that "solve without using trigonometric tables".
This basically means that we should not make use of trigonometric tables.
However, we can always use the trigonometric values of the standard angles (0, 30, 45, 60, 90 degrees).
We get these values by a proper proof which may or may not be possible for all the angles. So, we can make use of the standard values of trigonometric ratios.