A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 22, what is the area of the triangle?

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Answer 1 · 2018-03-26T07:39:48

Area of the rt. triangle #color(maroon)(A_t = (1/2) * a * b = 64.9 " sq units"#

#b = 22, hat A = pi/12, hat C = pi/2#

#hat B = pi - hat A - hat CC = pi - pi/12 - pi/2 = (5pi)/12#

Applying Law of sines,

#a / sin A = b / sin B = c / sin C#

#a = (b sin A) / sin B = (22 * sin (pi/12)) / sin ((5pi)/12) = 5.9#

It's a right triangle with #hat C = pi/2#

Hence area of the rt. triangle #A_t = (1/2) * a * b = (1/2) * 5.9 * 22 = 64.9 " sq units"#