Question

A triangle has sides A, B, and C. Sides A and B are of lengths `2` and `3`, respectively, and the angle between A and B is `pi/12`. What is the length of side C?

Answer 1

Third side is `1.187`

Explanation:

When two sides `a` and `b` and included angle `C` between them is given, the third side is given by cosine formula i.e. `c^2=a^2+b^2-2abcosC`.

Here, we have `a=2` and `b=3` and `C=pi/12=15°`,

Hence, `c^2=2^2+3^2-2×2×3×cos15°`

= `4+9-12×0.966`

= `13-11.592=1.408`

And `c=sqrt1.408=1.187`