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Question

If in a ΔABC,a=(1+3) cm,b=2cmand C=60 find the other two angles and the third side.

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Solution

we have , a=1+3,b=2 and C=60

Weknow that c2=a2+b22ab cos C

c2=(1+3)2+(2)22×(1+3)(2)cos 60

c2=1+3+23+44(3+1)×12

c2=8+23232=6

c=6

Using sine rule,

asin A=bsin B=csin C

1+3sin A=2sin B=6sin 60

2sin B=632sin B=12

B=45

We know the sum of all angles of a triangle is 180

A+B+C=180

A=180(B+C)

A=180(45+60)=75

HenceA=75,B=45,and,c=6


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