Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/8`. If side C has a length of `16` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

`A = 10.8 (3s.f.)`

Explanation:

sine rule:

`A/sin a = B/sin b = C/sin c`

the uppercase letters are sides, while the lowercase letters are angles opposite the sides.

angle `a` is the angle between `B` and `C`, angle `b` is the angle between `A` and `C`, and angle `c` is the angle between `A` and `B`.

angle between `A` and `B` = `pi/8`
angle between `B` and `C` = `pi/12`

`c = pi/8`
`a = pi/12`

`C = 16`

using the sine rule, `A/sin (pi/12) = 16/sin (pi/8)`

multiply by `sin (pi/12)`:

`A = (16sin(pi/12))/sin(pi/8)`

using a calculator with the radians (Rad) setting:

`A = 10.8 (3s.f.)`