A triangle has sides A,B, and C. If the angle between sides A and B is #(pi)/2#, the angle between sides B and C is #pi/6#, and the length of B is 18, what is the area of the triangle?

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Answer 1 · 2018-05-26T01:26:22

Area of triangle #color(crimson)(A_t = 93.51# sq units

#b = 18, hat A = pi/6, hat C = pi/2#

#hat B = pi - pi/6 - pi/2 = pi/3#

It’s a right triangle.

As per Law of Sines,

#a = (b sin A)/ sin B#

#a = (18 * sin (pi/6) )/ sin (pi/3) = 10.38#

Area of triangle #A_t = (1/2) a b sin C#

#A_t = (1/2) * 10.39 * 18 * sin (pi/2) = 93.51#