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 $hat B = hat C " & hence " b = c = 8$

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

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

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(pi)/12 and the angle between B and C is (5pi)/6 (5pi)/6. What is the area of the triangle?