SOLUTION: If a = 10 b= 20 and angle of C= 30 degrees solve for the missing pieces of the triangle: angle A= angle B= c=

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Question 930524: If a = 10 b= 20 and angle of C= 30 degrees solve for the missing pieces of the triangle:
angle A=
angle B=
c=
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If a = 10 b= 20 and angle of C= 30 degrees solve for the missing pieces of the triangle:
angle A=
angle B=
c=
***
law of cosine: c^2=a^2+b^2-2abcosC,a and b are the two sides with the included angle C, c=side opposite angle C.
law of sine: SinC/c=sinA/a, c and a are sides opposite angles C and A
..
c^2=10^2+20^2-2*10*20*cos30˚
c^2=100+400-400(√3/2)
c^2=500-346.41=153.60
c=12.4
..
sinC/c=sinB/b
12.4sinB=20sinC
sinB=20(1/2)/12.4
sinB=.8065
B=53.76˚
..
sinC/c=sinA/a
12.4sinA=10sinC
sinA=10(1/2)/12.4
sinA=.4032
A=23.78˚