SOLUTION: Solve the triangle using the given information. A=105degrees b=12 c=9 I'm pretty sure you need to use law of sines: because your given two sides and one angle. But I don't kn

Click here to see ALL problems on Trigonometry-basics

Question 684424: Solve the triangle using the given information.
A=105degrees
b=12
c=9
I'm pretty sure you need to use law of sines: because your given two sides and one angle.
But I don't know how to start. Please provide full steps
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
You use the law of cosines actually to find the length of 'a'

a^2 = b^2 + c^2 - 2*b*c*cos(A)

a^2 = 12^2 + 9^2 - 2*12*9*cos(105)

a^2 = 225 - 216*cos(105)

a^2 = 225 - 216*(-0.258819)

a^2 = 280.904904

a = sqrt(280.904904)

a = 16.76021789

Now that you know that

a = 16.76021789
b = 12
c = 9

You can use the law of sines to find angles B and C. I'll show you how to find angle B and I'll let you find angle C

sin(B)/b = sin(A)/a

sin(B)/12 = sin(105)/16.76021789

sin(B)/12 = 0.9659258/16.76021789

sin(B)/12 = 0.0576321

sin(B) = 12*0.0576321

sin(B) = 0.6915852

B = arcsin(0.6915852)

B = 43.7557225

So the angle B is roughly 43.7557225 degrees

I'll let you find angle C

Note: there are 2 ways to find angle C, you can use the fact that A+B+C = 180 (ie all angles must add to 180) or you can use the law of sines again.