A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4#. If side C has a length of #6 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2018-02-28T12:06:33

Length of sides #A and B# are # 7.84 ,7.84 # unit respectively.

Angle between Sides # A and B# is # /_c= pi/4=180/4=45^0#

Angle between Sides # B and C# is # /_a= (3pi)/8=67.5^0 :.#

Angle between Sides # C and A# is

# /_b= 180-(45+67.5)=67.5^0 ; C=6#

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=6 :. B/sinb=C/sinc# or

#B/sin67.5=6/sin45 or B= 6* (sin67.5/sin45) ~~ 7.84 (2dp) #

Similarly #A/sina=C/sinc:. A/sin67.5=6/sin 45# or

#A= 6* (sin 67.5/sin45) ~~ 7.84 (2dp) #

Length of sides #A and B# are # 7.84 ,7.84 # unit respectively.[Ans]