Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/12`. If side C has a length of `25` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

`a = 25`

Explanation:

Let's state this problem in standard notation where the lengths of the sides are lowercase letters, a, b, and c, and the angles opposite the corresponding side are uppercase letters, A, B, and C, respectively.

The angle between sides a and b is angle C:

`C = pi/12`

`c = 25`

The angle between sides b and c is angle A:

`A = pi/12`

Ordinarily, one would use the law of sines:

`a/sin(A) = c/sin(C)`

but, because A = C we know that a = c. Therefore, a = 25.