A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/3$ . If side C has a length of $16$ and the angle between sides B and C is $( pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2017-07-13T09:41:15

The sides $a=7.07$ and $b=18.32$

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The angle $hat(ACB)=1/3pi$

The angle $hat(BAC)=1/8pi$

The side $c=16$

The angle $hat(ABC)=pi-(1/3pi+1/8pi)=pi-11/24pi=13/24pi$

We apply the sine rule to the triangle $DeltaABC$

$a/sin(hat(BAC))=b/sin(hat(ABC))=c/sin(hat(ACB))$

$a/sin(1/8pi)=b/sin(13/24pi)=16/sin(1/3pi)=18.48$

Therefore,

$a=18.48*sin(1/8pi)=7.07$

$b=18.48sin(13/24pi)=18.32$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/3(pi)/3. If side C has a length of 16 16 and the angle between sides B and C is ( pi)/8( pi)/8, what are the lengths of sides A and B?