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 25, what is the area of the triangle?

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Answer 1 · 2018-03-16T03:56:55

Area of the triangle #~~ 83.73# sq units

#hatC = pi / 2, hat A = pi / 12, hat B = pi - pi / 12 - pi / 2 = (5pi) / 12, b = 25#

It's a right triangle.

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#a / sin (pi/12) = c / sin (pi/2) = 25 / sin ((5pi)/12)#

#a = (25 * Sin (pi/12) ) / sin((5pi)/12) ~~ 6.7#

#Area = (1/2) a * b = (25 * 6.7) / 2 ~~ 83.73#

since it's a right triangle with #hatC = pi/2#