# 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

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 " #