A triangle has sides A,B, and C. If the angle between sides A and B is (7pi)/12, the angle between sides B and C is pi/6, and the length of B is 5, what is the area of the triangle?

1 Answer
Leland Adriano Alejandro
Jan 22, 2016

Area=8.53766 square units

Explanation:

From the given, two angles A=pi/6, C=(7pi)/12 and included side b=5. Try drawing the triangle. See that angle B=pi/4 by computation using the formula A+B+C=pi. Also , the altitude from angle C to side c can be called height h is h = b*sin (pi/6)=2.5
Side c can be computed using formula c=b*cos A+h*cot B.
c=5*cos (pi/6)+2.5*cot (pi/4)=2.5*(sqrt3+1)

c=2.5(sqrt3+1)
Area can now be computed

Area=1/2*b*c*sin A

Area=1/2*5*(2.5(sqrt3+1))*sin (pi/6)

Area=8.53766 square units

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