So i have a triangle with sides 10 and 40, and the angle between them is 70 degrees. I don't know any other measurements of this triangle.
I use cosine law to find the 3rd side, which turns out to be 37.8.
Then I found the other 2 angles with sine law, and I obtain 14 degrees and 84 degrees.
However, the weird thing is the three angles do not add up to 180!!
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.
Because, in a triangle, the smallest angle is always less than (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).and how come for 14 degrees, there isnt another angle of 180-14?
So the angle is the smallest angle here, because it's opposite the shortest side. And so it's , not .