Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/6`, the angle between sides B and C is `(5pi)/12`, and the length of B is 7, what is the area of the triangle?

Answer 1

`color(purple)("Area of " Delta, A_t = 12.25 " sq units"`

Explanation:

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

It's an isosceles triangle with sides a & b equal.

Given `b = 7 " and hence " a " also " = 7`

`"Area of " Delta, A_t = (1/2) a b sic C`

`color(purple)(A_t = (1/2) 7^2 sin (pi/6) = 49/4 = 12.25 " sq units"`