Question

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

Answer 1

Area = 18 units

Explanation:

The given triangle is sketched as in the figure above. Angle B would be `pi -pi/12 -(5pi)/12 = pi/2`

Side b is 12. It is the hypotenuse because it is opposite the right angle B.

For area, base and altitude is required. In this case it is side 'a' and side 'c'.

Side 'c' = `12 cos (pi/12)`

Side 'a' = `12 sin (pi/12)`

Area = `1/2 (12 sin (pi/12) *12 cos (pi/12))`
=`72 sin (pi/12) cos (pi/12)` =`36 (2sin (pi/12) cos (pi/12))`= 36 sin pi/6= 36`1/2`= 18

Area = 18 units.