Question

Find a.Round to the nearest tenth:a10 cm150°12°a = [? ]cmLaw of Sines: sin Asin Bsin C-abС

Answer 1

Here we have a direct application of the Law of Sines. Side a is opposite to angle 150°, while the side measuring 10 cm is opposito the the angle 12°. So, applying the Law of Sines:

`\begin{gathered} (\sin150\degree)/(a)=(\sin 12\degree)/(10) \\ 10\sin 150\degree=a\sin 12\degree \\ a=(10\sin150\degree)/(\sin12\degree)=(10\cdot0.5)/(0.20791169\ldots)=24.0486\ldots\approx24.0 \end{gathered}`

So, the measure of a is approximately 24.0 cm.