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enter image description here $\angle BCA=90$ degrees

I probably do not understand the concept of angle sum in a triangle but here is the thing. $\angle BAC$ is negative by convention. So is $BCA$ going to be greater than 180 degrees?

So this is obviously wrong(or is it?). I suppose you should take only the magnitude of the angle into account. Can someone tell me when you should consider the sign and when you should not?

snulty
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The Cryptic Cat
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  • Angle BAC is only negative because of its "direction", not by its magnitude. When we looks at the sum of the angles in a triangle, when look at their magnitudes. The sum of the angles in any triangle (drawn on a flat surface) is equal to 180° – imranfat Mar 04 '16 at 16:07
  • Just as a note, the convention only applies to angles that are made with the x-axis, so for example, you couldn't conclude anything about $\angle ABC$ as to whether its positive or negative? So that convention shouldn't be used here. It is however useful for dealing with the unit circle for example. – snulty Mar 04 '16 at 16:11
  • @imranfat Maybe you misinterpreted what I said because I think that is what I guessed. Could you tell me why introducing negative angles proves useful? – The Cryptic Cat Mar 04 '16 at 16:11
  • Study the topic of inverses with respect to sine and tangent and it will become clear... – imranfat Mar 04 '16 at 16:21
  • Every angel is defined actually as "angel"+nX360, n being an whole number - so, clockwise direction reduces the value of "angel" and by selecting n large enough any angel may be expressed as a negative angel, BAC – Moti Mar 04 '16 at 22:30

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