ANSWER
The value of theta in the second quadrant is,
[tex]143.1 \degree[/tex]
EXPLANATION
The given trigonometric equation is
[tex] \sin( \theta) = \frac{3}{5} [/tex]
This implies that,
[tex] \theta= arcsin(\frac{3}{5} )[/tex]
This implies that the principal solution is
[tex] \theta = 36.9 \degree[/tex]
and it is an angle in the first quadrant.
But the solution we are looking for is an angle in the second quadrant.
This is given by
[tex]180 - \theta = 180 - 36.9 = 143.1 \degree[/tex]
