Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/3`. If side C has a length of `24` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

6.00

Explanation:

Length c = 24, angle C = π/3. Angle A = π/12 (calculations in radians)
The Law of Sines (or Sine Rule) is very useful for solving triangles:
`(a/sin A) = (b/sin B) = (c/sin C)`

a/sin(π/12) = 24/sin(π/3)

a = 24/sin(π/3) * sin(π/12) ; a = 22.9 * 0.262 = 6.00s

We can similarly then find the length of b to be 42 (the angle of B must be `(7π/12)`.)