A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6. If side C has a length of 36 and the angle between sides B and C is pi/12, what are the lengths of sides A and B?

1 Answer
Mar 10, 2016

=> A = B ~~ 18.635 to 3 decimal places

Explanation:

A Diagram always helps!

Tony B

Known: The sum of the internal angles is pi radians (180^o)

Thus the angle between A and C is pi-pi/12-(5pi)/6 = pi/12

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color(blue)("Using the sine rule")

C/(sin(/_AB)) =B/(sin(/_AC))=A/(sin(/_BC))

Also as /_AC = /_BC then length A=B

C/(sin(/_AB)) = 36/(sin((5pi)/6))= A/(sin( pi/12))

=>A = (sin(pi/12))/(sin((5pi)/6))xx36

=> A = B ~~ 18.635 to 3 decimal places