Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(7pi)/8`, the angle between sides B and C is `pi/12`, and the length of B is 1, what is the area of the triangle?

Answer 1

Area of the triangle is `0.3794`

Explanation:

As two angles are `(7pi)/8` and `pi/12`,

third angle between sides A and C is `pi-(7pi)/8-pi/12=pi/24`

Now using sine formula for triangles, we have

`A/sin(pi/12)=C/sin((7pi)/8)=B/sin(pi/24)` and as `B=1`

we have `A/0.25882=C/0.38268=1/0.13053=7.661`

Hence `A=7.6611xx0.25882=1.983` and

`C=7.6611xx0.38268=2.932`

As area of a triangle is given by `1/2bcsinA`

Area of the triangle is `1/2xx1xx2.932xx0.25882=0.3794`