Trigonometry
What you must know
In right-angled triangles use Pythagoras and SOHCAHTOA: sin theta = opposite/hypotenuse, cos theta = adjacent/hypotenuse, tan theta = opposite/adjacent. Find sides by multiplying, and angles by using the inverse functions. Learn exact values for 30, 45 and 60 degrees. Apply angles of elevation and depression, and interpret three-figure bearings measured clockwise from north. For non-right-angled triangles use the sine rule a/sin A = b/sin B = c/sin C, the cosine rule a^2 = b^2 + c^2 - 2bc cos A, and area = half ab sin C. Choose the cosine rule when you have two sides and the included angle, or all three sides; choose the sine rule when you have a matching side-and-angle pair.
Traps
- Calculator in the wrong mode: check it shows DEG.
- The sine rule for an angle can produce an ambiguous obtuse solution.
- The angle used in the cosine rule must lie between the two known sides.
- A back-bearing differs by 180 degrees; adjust if the result exceeds 360 degrees or is negative.
- Round only at the final step; keep full calculator values in the display.
Rule of thumb
Label the triangle so that side a is opposite angle A, and so on. Then ask which rule matches the information you have.
Example: with b = 7, c = 9 and A = 50 degrees, a^2 = 49 + 81 - 2(7)(9)cos 50 degrees, which is about 49.0, so a is about 7.0.