Question

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

Answer 1

`"Area"_triangle=color(green)((9sqrt(3))/4)`

Explanation:

As can be seen from the image below, the given triangle can be split into 2 triangles with angles: `pi/6, pi/3, and pi/2`
This is the ratios for one of that standard trigonometric triangles
we can see that the height of the original triangle must be `color(red)(3/2 *sqrt(3))`

and the triangle's area will be:
`color(white)("XXX")1/2 * b * h = 1/2 xx 3 xx((3sqrt(3))/2)=(9sqrt(3))/4`