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 $2$ 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 · 2017-07-04T07:50:34

The lengths of the sides are $A=0.88$ and $B=2.29$

We apply the sine rule to the triangle $ABC$ .

$A/sin hat A=B/sin hat B=C/ sin hatC$

The angle $hat B$ is

$=pi-(hatA+hatC)$

$=pi-(1/3pi+1/8pi)=pi-11/24pi=13/24pi$

Therefore,

$A/sin(1/8pi)=B/sin(13/24pi)=2/sin(1/3pi)=2.31$

$A=2.31*sin(1/8pi)=0.88$

$B=2.31*sin(13/24pi)=2.29$

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 2 2 and the angle between sides B and C is ( pi)/8( pi)/8, what are the lengths of sides A and B?