If sides A and B of a triangle have lengths of 3 and 12 respectively, and the angle between them is #(pi)/6#, then what is the area of the triangle?

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Answer 1 · 2016-01-27T09:51:40

#Area=9# square units

Use the formula for Area of a triangle when two sides and included angle are given

#Area = 1/2*a*b*sin C#
#Area = 1/2*b*c*sin A#
#Area = 1/2*a*c*sin B#

All of the above are always true.

Given : #a=3# and #b=12# and #Sin C=Sin (pi/6)=1/2#

Use #Area = 1/2*a*b*sin C#

#Area=1/2*3*12*1/2#

#Area=9# square units