Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4` and the angle between sides B and C is `pi/12`. If side B has a length of 7, what is the area of the triangle?

Answer 1

1. Sum of angles in a triangle, followed by
2. Sin rule

Explanation:

since we know 2 angles of the triangle and the length of one side of the triangle (assuming it is measured in centimetres), the first step we can take is

`pi` - `(3pi)/4` - `(pi)/12` = 3rd unknown angle, `x`

We can then apply the sin rule to find the length of either A or C (I'll go with C)

`C/sin((3pi)/4)` = `7/sin(x)`

area of the triangle = 0.5 (7)(C)`sin(pi/12)`