A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is #(pi)/12# and the angle between B and C is # (5pi)/6#. What is the area of the triangle?

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Answer 1 · 2018-03-27T02:52:55

#color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"#

#a = 5, b = 8, hat A = (5pi)/6, hat B = pi/12#

To find the area of the triangle.

#hat C = pi - (5pi)/6 - pi/12 = pi/12#

It's an isosceles triangle with #hat B = hat C " & hence " b = c = 8#

Formula for Area of triangle, knowing 2 sides and included angle

#color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"#