Question

Calculate the value of angle A and C of ∆ ABC. Where b=1435cm, a= 782cm and B= 115.6°.​

Answer 1

The Law of Sines says

$\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}$

$\sin A = \dfrac a b \sin B$

$A = \arcsin( \dfrac{782}{1435} \sin 115.6 ) = 29.44^\circ$

We don't have to worry about the obtuse supplement because a triangle can only have one obtuse angle, and that's B.

$C = 180 - 115.6 - 29.44 = 34.96^\circ$

Answer: A=29.44°, C=34.96°