Hello tea123456 Originally Posted by

**tea123456** can i ask why there are 2 angles that results the same sine value?

I don't know how far your study of trigonometry has gone, but if you're using the Sine and Cosine Rules, you need to know how to handle obtuse angles. The rules are: $\displaystyle \sin(180^o - \theta)=\sin \theta $

and

$\displaystyle \cos(180^o - \theta)=-\cos \theta $

To understand the reasons for these rules, you'll need to look at the definitions of sine and cosine for angles of any size. These are based on the *unit circle*. You may find this page helpful.

and how come for 14 degrees, there isnt another angle of 180-14?

Because, in a triangle, the smallest angle is always less than $\displaystyle 90^o$ (obviously!) and it is always opposite the shortest side (because of the Sine Rule, where each side is in proportion to the sine of the opposite angle).

So the $\displaystyle 14^o$ angle is the smallest angle here, because it's opposite the shortest side. And so it's $\displaystyle 14^o$, not $\displaystyle 166^o$.

Grandad