Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(3pi)/4`, the angle between sides B and C is `pi/6`, and the length of B is 7, what is the area of the triangle?

Answer 1

`color(blue)("Area of Triangle " A_t = color(indigo)(33.46 " sq units"`

Explanation:

`hat A = pi/6, hat C = (3pi)/4, b = 7, " To find area of " Delta`

`hat B = pi - pi/6 - (3pi)/ 4 = pi/12`

Applying the Law of Sines,

`a / sin (pi/6) = 7 / sin (pi/12) = c / sin ((3pi) / 4)`

`a = (7 * sin (pi/6) ) / sin (pi/12) = 13.52`

Now we know two sides and the included angle.

`:. "Area of " Delta = A_t = (1/2) a b sin C`

`A_t = (1/2) * 13.52 * 7 * sin ((3pi)/4) = color(indigo)(33.46 " sq units"`