A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/6#. If side C has a length of #1 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?

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Answer 1 · 2016-06-13T15:23:56

side #a=0.517638" "#unit

side #b=0.517638" "#unit

The triangle is isosceles with angles #A=B# and therefore sides #a=b#

with angle #C=(5pi)/6# and angle #A=B=pi/12#

also side #c=1#

Using Sine Law

#a/sin A=b/sin B=c/sin C#

Solve side #a#

#a=c*sin A/sin C=1*sin (pi/12)/sin ((5pi)/6)=0.517638#

it follows

#b=a=0.517638#

God bless...I hope the explanation is useful.