Choose the angle first, then identify opposite, adjacent and hypotenuse. The hypotenuse is opposite the right angle. sintheta= oppositehypotenuse, = adjacenthypotenuse, = oppositeadjacent Side a is opposite A, side b opposite B, and side c opposite C. Thus C= ACB. **Given information** | **Useful rule** A side and its opposite angle, with another side or angle | asin A= bsin B= csin C Two sides and their included angle | c2=a2+b2-2abcos C Three sides | cos C= a2+b2-c22ab Two sides and their included angle, for area | Area= 12absin C Check the angle unit and whether the angle lies between the sides used in the area formula. Keep full calculator precision until the final answer.

Choose the angle first, then identify opposite, adjacent and hypotenuse. The hypotenuse is opposite the right angle.

\(\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}},\quad\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}},\quad\tan\theta=\dfrac{\text{opposite}}{\text{adjacent}}\)

Side \(a\) is opposite \(A\), side \(b\) opposite \(B\), and side \(c\) opposite \(C\). Thus \(C=\angle ACB\).

A side and its opposite angle, with another side or angle

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

Two sides and their included angle, for area

Check the angle unit and whether the angle lies between the sides used in the area formula. Keep full calculator precision until the final answer.

Trigonometry

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Triangle Ratios and Rules

Triangle Ratios and Rules