Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/3` and the angle between sides B and C is `pi/12`. If side B has a length of 5, what is the area of the triangle?

Answer 1

Area of triangle is `2.90`

Explanation:

The third angle opposite sides `A` and `C` is

`pi-pi/3-pi/12=(12-4-1)pi/12=5pi/12` and it has side `B=5` opposite it.

As side `A` has angle opposite it `pi/12`, using sine formula, we get

`A/sin(pi/12)=B/sin((5pi)/12)` or

`A=Bxxsin(pi/12)/sin((5pi)/12)=5xx0.2588/0.9659=1.34`

Hence area of triangle is `1/2xx5xx1.34xxsin(pi/3)`

= `1/2xx5xx1.34xx0.866=2.90`