Question

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?

Answer 1

≈ 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 "`