Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(pi)/3`, the angle between sides B and C is `pi/6`, and the length of B is 9, what is the area of the triangle?

Answer 1

17.537

Explanation:

As the sum of all the angles of a triangle is `180^0` or `pi` radians
So, from your sum it can be seen that the third angle between A and C `=pi-pi/3-pi/6=pi/2`
Thus making the side B, which is opposite to the `90^0` angle hypotenuse of the triangle.
So, the area of the triangle would be `1/2*base*height=1/2*A*C`
Given that side `B=9`, we can find the other two side by triangle geometry
`A=B*cos(pi/3)=9*cos(pi/3)=4.5`
`C=B*sin(pi/6)=9*sin(pi/6)=7.794`
Hence, `Area=1/2*A*C=1/2*4.5*7.794=17.537`