Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(3pi)/8`, the angle between sides B and C is `pi/12`, and the length of B is 5, what is the area of the triangle?

Answer 1

Hence area of triangle is `3.015` units

Explanation:

The length of side `B` is `5` and angle opposite this side is angle between sides `A` and `C`, which is not given. But as other two angles are `(3pi)/8` and `pi/12`, this angle would be

`pi-(3pi)/8-pi/12=(24pi-9pi-2pi)/24=(13pi)/24`

Now for using sine formula for area of triangle given by `1/2xxabxxsintheta`, we need one more side. Let us choose the side `C`, which is opposite the angle `(3pi)/8`.

Now using sine rule we have

`5/sin((13pi)/24)=C/sin((3pi)/8)` or `C=5xxsin((3pi)/8)/sin((13pi)/24)`

Hence area of triangle is `1/2xx5xx5xxsin((3pi)/8)/sin((13pi)/24)xxsin(pi/12)`

= `25/2xx(0.9239xx0.2588)/0.9914=3.015` units