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 26, what is the area of the triangle?

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Answer 1 · 2018-02-17T04:19:52

#A_t = (1/2) b h = color (green)(90.5668)#

#hatA = pi/12, hatC = pi/2, b = 26#

#hatB = pi - (pi/2 - pi/12) = (5pi)/12#

It’s a right triangle. Hence, area #A_t = (1/2) a * b#

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To find side a

#a / sin A = b / sin B#

#a = (26 * sin (pi/12)) / sin ((5pi)/12) = 6.9667#

#A_t = (1/2) * 6.9667 * 26 = color (green)(90.5668)#