I'm having a hard time finding the solution of the bearing given in our example.
Our Example: Suppose there's a triangle with points named A,B, and C.
Point A is named Bacoor. Point B is named San Pablo. Point C is named Sto. Tomas.
The Distance: AB = 60.5 km ; BC = 20.9 km ; AC = 44.4 km ;
The bearings:
San Pablo, Laguna = *46.42SE of Bacoor Cavite
Sto. Tomas, Batangas = *61.19 SE of Bacoor Cavite
I don't know why the bearings are 46.42 and 61.19. Can you please help me or give me a hint with the solution? Thanks.
P.S. here are the angles.
cos A = 14.77 cos B = 32.80 cos C = 132.43
The data you give does not allow the calculation of the bearings. You can get the three angles $A,B,C$ using the law of cosines. From the data you have, the triangle could be oriented any way on the earth's surface.
If I look on the map, it looks like the line from Bacoor to Sto. Tomas is at an angle of about 60 degrees South of East, and San Pablo is at an angle of about 45 degrees South of East.