Right-angled trigonometry, the sine rule and the cosine rule

Learning objectives

Use the sine, cosine and tangent ratios and Pythagoras' theorem to find unknown sides and angles in a right-angled triangle

Apply the sine rule a/sin A = b/sin B to find a side or an angle in a non-right-angled triangle, checking an angle found from its sine against the triangle (the two-triangle ambiguous case is HL only and is not part of this course)

Apply the cosine rule a² = b² + c² − 2bc cos A to find a third side, and its rearrangement cos A = (b² + c² − a²)/(2bc) to find an angle when three sides are known

Calculate the area of a triangle using ½ab sin C, and use it to find a missing side or the included angle

Choose the appropriate rule for a given triangle by identifying which sides and angles are known, and work with unrounded intermediate values throughout a multi-step problem