A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #18 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-11-17T11:05:20

Length of side #A# is #4.66(2dp)# unit.

Angle between Sides # A and B# is # /_c= pi/2=180/2=90^0#

Angle between Sides # B and C# is # /_a= pi/12=180/12=15^0 :.#

Angle between Sides # C and A# is # /_b= 180-(90+15)=75^0#

The sine rule states if #A, B and C# are the lengths of the sides

and opposite angles are #a, b and c# in a triangle, then:

#A/sina = B/sinb=C/sinc ; C=18 :. A/sina=C/sinc# or

#A/sin15=18/sin90 :. A = 18* sin15/sin90 ~~ 4.66(2dp)#unit

Length of side #A# is #4.66(2dp)#unit. [Ans]