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

1 Answer
Binayaka C.
Apr 15, 2017

Length of sides B and C are #9.66# unit each.

Explanation:

The angle between sides A and B is # /_c = pi/6=180/6=30^0#
The angle between sides B and C is # /_a = (5pi)/12=(5*180)/12=75^0#
The angle between sides C and A is # /_b = 180-(30+75)=75^0#

We know by sine law #A/sina=B/sinb=C/sinc ; C= 5,/_a=75^0,/_b=75^0,/_c=30^0 #

#:. A/sin75 = C/sin30 or A= 5 * sin 75/sin30 ~~ 9.66 (2dp)#. Similarly

#:. B/sin75 = C/sin30 or B= 5 * sin 75/sin30 ~~ 9.66 (2dp)#

Length of sides B and C are #9.66# unit each.[Ans]

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