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Area of Triangles Non Right-Angled Triangle Trigonometry By the end of this lesson you will be able to explain/calculate the following: 1. Area of Right-Angled Triangles 2. Area of Non Right-Angled Triangles • Often the triangle that is identified in a given problem is non–right-angled. • Thus, Pythagoras’ theorem or the trigonometric ratios are not as easily applied. • The two rules that can be used to solve such problems are: 1. the sine rule, and 2. the cosine rule. • For the sine and cosine rules the following labelling convention should be used. ▫ Angle A is opposite side a (at point A) ▫ Angle B is opposite side b (at point B) ▫ Angle C is opposite side c (at point C) ▫ To avoid cluttered diagrams, only the points (A, B and C) are usually shown and are used to represent the angles A, B & C. opp sin hyp h sin C b h b sin C • We can use the area formula to find the included angle between two sides • We need to use the inverse sine ratio ▫ denoted as sin-1 • A triangle has sides of length 10 cm and 11 cm and an area of 50 cm2. Show that the included angle may have two possible sizes.