Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 9, what is the area of the triangle?

Answer 1

`color(crimson)("Area of " Delta = 20.25 " sq units"`

Explanation:

`hat A = pi/12, hat C = (5pi) / 6, hat B = pi/12, b = 9`

`color(blue)("As angles " hat A , hat B " are equal, their sides will also be equal "`

`color(blue)(" and the " Delta " is isosceles"`

`:. a = b = 9`

`"Area of " Delta = (1/2) a b sin C = (1/2) * 9^2 * sin ((5pi)/6)`

`color(crimson)("Area of " Delta = 20.25 " sq units"`