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A triangle has sides A,B, and C. If the angle between sides A and B is #(pi)/4#, the angle between sides B and C is #pi/6#, and the length of B is 1, what is the area of the triangle?

1 Answer

sankarankalyanam

Aug 10, 2018

#color(indigo)(A_t = 1/2 a b sin C ~~ 0.183, " sq. units"#

Explanation:

#hat A = pi/6, hat C = pi/4, hat B = (7pi)/12, b = 1#

Law of Sines : #a / sin A = b / sin b = c / sin C#

#a = (b * sin A) / sin B = (1 * sin (pi/6)) / sin ((7pi)/12)#

#a ~~ 0.5176#

#"Area of D" Delta = A_t = 1/2 a b sin C #

#color(indigo)(A_t = 1/2 * 0.5176 * 1 * sin (pi/4) ~~ 0.183, " sq. units"#

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