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 #3 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?

1 Answer
Binayaka C.
Oct 18, 2016

#A=1.55(2dp) unit ; B=1.55(2dp) unit ;#

Explanation:

The angle between sides A and B is #/_c = (5*180/6)=150^0#
The angle between sides B and C is #/_a = (180/12)=15^0#
The angle between sides C and A is #/_b = 180-(150+15)=15^0 ;C=3#
Applying sine law;# A/sina=B/sinb=C/sinc# we get #A/sin15=3/sin150 or A=3*(sin15/sin150)=1.55(2dp) unit# and similarly we get #B/sin15=3/sin150 or B=3*(sin15/sin150)=1.55(2dp) unit# {Ans]

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