If sides A and B of a triangle have lengths of 18 and 12 respectively, and the angle between them is $\frac{2 π}{3}$ $(2pi)/3$ , then what is the area of the triangle?

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Answer 1 · 2018-07-08T14:46:57

Area of triangle $A_{t} = 93.53$ $color(chocolate)(A_t = 93.53$ sq. units

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

Given $a = 18, b = 12, ˆ C = \frac{2 π}{3}$ $a = 18, b = 12, hat C = (2pi)/3$

$A_{t} = (\frac{1}{2}) \cdot 18 \cdot 12 \cdot sin (\frac{2 π}{3})$ $A_t = (1/2) * 18 * 12 * sin ((2pi)/3)$

$A_{t} = \frac{9 \cdot 12 \cdot \sqrt{3}}{2} = 54 \sqrt{3} = 93.53$ $A_t =( 9 * 12 * sqrt3) / 2 = 54 sqrt3 = 93.53$

If sides A and B of a triangle have lengths of 18 and 12 respectively, and the angle between them is 2π3(2pi)/3, then what is the area of the triangle?