Math Help - Trig navigation problem

1. Trig navigation problem

A lighthouse A bears N 36 degrees 20 minutes E at a ship S. After sailing 2.75 km in the direction N 78 degrees 50 minutes to point T, the bearing of the lighthouse becomes N 8degrees 30 minutes E. Find the distance from A to T.

2. let a = the distance from A to T

law of sines ...

$\frac{a}{\sin(42^{\circ} \, 30')} = \frac{2.75}{\sin(27^{\circ} \, 50')}$

double check my angle calculations