A triangle has sides A, B, and C. The angle between sides A and B is pi/6 and the angle between sides B and C is pi/12. If side B has a length of 2, what is the area of the triangle?

1 Answer
Jim G.
Mar 3, 2016

≈ 0.366 square units

Explanation:

I recommend you make a sketch.

Area can be calculated using either of the following formulae.

area = 1/2ABsin(pi/6) " or " 1/2BCsin(pi/12)

depending on which is used A or C will be required.

choose side A : Require use of color(blue)" sine rule "

The angle between A and C will also be required before progressing.

angle between A and C = pi - (pi/6 + pi/12 ) = (3pi)/4

sine rule : A/(sin(pi/12)) = B/(sin((3pi)/4))

rArr A = (2sin(pi/12))/(sin(3pi)/4) ≈ 0.732

rArr" area " = 1/2ABsin(pi/6) ≈ 0.366 " square units "

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