Question

Hello! I need help with this question. I know that I'm using the Law of Sines, but I'm confused on how to solve. I have to also round my answers to the nearest tenth for degrees and to the nearest hundredth for sides. Thanks!

Given:
A = 60 degrees
a = 9
c = 10


Find:
b=
C=
B=

Answer 1

Sine rule states that:
sin(A)/a = sin(B)/b = sin(C)/c

Here you are given both a and A, so knowledge of c will let you solve for sin(C).
Sin(C)=c*(sin(A)/a)=0.96225
and sin^-10.96225=74.207° or 105.793° since sin(x) is symmetrical about 90°.

If the sum of the larger angle (>90°, i.e. 105.793) and the known angle (60°) exceeds 180° then the larger angle can be rejected.

This is not the case in this problem, so the solution of this triangle has two solutions using the sine rule:
A=60, C=74.207, B=180-A-C
or
A=60, C=105.793, B=180-A-C.

The corresponding third side (b) can be found again using the sine rule once B is known.