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 #( pi)/2#, what are the lengths of sides A and B?

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Answer 1 · 2018-07-24T13:15:19

#A=10# & #B=5\sqrt3#

The angle between sides #A# & #C#

#=\pi-\frac{\pi}{6}-\pi/2#

#=\pi/3#

Now, using Sine rule in the given triangle as follows

#\frac{A}{\sin(\pi/2)}=\frac{B}{\sin(\pi/3)}=\frac{C}{\sin(\pi/6)}#

#\frac{A}{1}=\frac{B}{\sqrt3/2}=\frac{5}{1/2}#

#A=2/\sqrt3 B=10#

#\implies A=10# &

#B=\sqrt3/2\times 10#

#=5\sqrt3#