# trig

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What is the angle B?

Given that
A=46 degree
b=4
c=8

• trig -

Is this a triangle?

Law of Cosines:

a^2=b^2+c^2-2bcCosA
solve for a.
Then, law of sines:

sin46/a=sinB/b
solve for sinB, then B

• trig -

LAW OF COSINES: CosA=(b^2+c^2-a^2)/2bc

Cos46=(16+64-a^2)/2*4*8.
Cos46=(80-a^2)/64, 80-a^2=64Cos46,
a^2=80-64Cos46=35.54, a=5.96=6.0

LAW of SINES: SinB/b=SinA/a

SinB/4=Sin46/6,Multiply both sides by 4: SinB=4*Sin46/6=0.4791, B=28.66=28.7

• trig -

and easy way to check this is to grab your protractor and sketch it to see if it works.

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