AI Study GuruUnderstand the idea
In a right angled triangle, name the sides relative to an acute angle: opposite, adjacent and hypotenuse. Sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. A memory aid is SOH CAH TOA. Memorise the standard angles: sine 30 is one half, cosine 60 is one half, and tangent 45 is 1. Always check the triangle is right angled and that you labelled sides against the correct angle before computing.
See a worked example
With opposite 3 and hypotenuse 5, sine equals 3 over 5. With adjacent 4 and hypotenuse 5, cosine equals 4 over 5, and tangent equals 3 over 4. For a 45 degree angle in an isosceles right triangle, tangent 45 equals 1 since opposite and adjacent match.
A useful check
The classic error is mixing up opposite and adjacent, especially after switching to the other acute angle. Redraw and relabel for the angle you are using. Another error is applying ratios to triangles without a right angle; they only work when one angle is 90 degrees.
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