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How do you find the area of the triangle given #C=120^circ, a=4, b=6#?

1 Answer

sankarankalyanam

Mar 7, 2018

Area of triangle #color(red)(A_t = 6 sqrt3 = 10.39# sq units

Explanation:

Area of a triangle can be calculated using formula

#A_t = (1/2) a b sin C# having known SAS measurements.

#Given : a = 4, b = 6, hatC = 120^@#

#A_t = (1/2) 4 * 6 * sin 120 = (1/cancel2) * cancel(24)^color(red)(12) * sin (180 - 120)#

#A_t = 12 * sin 60 =( (cancel(12 )^color(red)(6) * sqrt3 ) / cancel2) = 6 sqrt3#

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