If sides A and B of a triangle have lengths of 12 and 8 respectively, and the angle between them is $\frac{5 π}{6}$ $(5pi)/6$ , then what is the area of the triangle?

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Answer 1 · 2018-06-03T11:47:07

Area of triangle $A_{t} = 24$ $color(green)(A_t = 24$ sq units

Given : $a = 12, b = 8, ˆ C = \frac{5 π}{6}$ $a = 12, b = 8, hat C = (5pi)/6$

Formula for area of triangle $A_{t} = (\frac{1}{2}) a b sin C$ $A_t = (1/2) a b sin C$

$A_{t} = (\frac{1}{2}) \cdot 12 \cdot 8 \cdot sin (\frac{5 π}{6}) = 24$ $A_t = (1/2) * 12 * 8 * sin ((5pi)/6) = 24$ sq units

If sides A and B of a triangle have lengths of 12 and 8 respectively, and the angle between them is 5π6(5pi)/6, then what is the area of the triangle?