A triangle has sides A, B, and C. Sides A and B are of lengths #4# and #2#, respectively, and the angle between A and B is #(5pi)/6 #. What is the length of side C?

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Answer 1 · 2018-05-11T11:32:47

The length of side #C# is #5.82 # unit.

Angle between Sides # A and B# is # /_c= (5 pi)/6#

#=(5*180)/6=150^0#

Sides #A=4 , B=2 , C = ? # Cosine rule: (for all triangles)

#C^2= A^2 + B^2 − 2 A B cos c #

#:. C^2=4^2 + 2^2 − 2*4*2*cos150# or

#C^2~~33.86 :. C ~~ 5.82 (2 dp)#

The length of side #C# is #5.82 # unit [Ans]