13y = 15x
tangent = y / x for an angle in the first quadrant, Q1.
The reference angle forms a right triangle with a base of x and a height of y.
From the equation 13y = 15x y = 15x / 13 y/x = 15/13 tan (theta) = 15/13
Find the Arctan (15/13), which = tan^(-1) (15/13) = 49 degrees to two significant digits
49 degrees * ( pi radians / 180 degrees ) = 0.86 radians to two significant digits
Firstly there is no theta in the question but it is pretty obvious that you want the gradiant of the line and jjzamball has found that for your nicely.
the only comment I would make to jjzamball is that if you change one unit to another unit and you want your answer correct to 2 signif figures then the original unit should have more than 2 significant figures or you a likely to end up with too much rounding error.
It is just a little observation.