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Trigonometry in Non-Right Angled Triangles Area of a Triangle You need to know 2 sides and the angle in between. Example:- Calculate the area of this triangle. Area = ½ ab Sin C = ½ x 16 x 16 x Sin 35o = 73.4177… = 73.4 cm2 Sine Rule Look for pairs of angles and sides. Need to know one pair (angle and side) plus angle/side opposite required side/angle. Example:- Find the length of the missing side, x cm. Example:- Find the size of the missing angle, xo. Always to 3 decimal places!! Remember to use SHIFT SIN => 𝑥 = 𝑠𝑖𝑛−1 0.945 = 70.8𝑜 . Cosine Rule To find a missing side To find a missing angle Use the Cosine rule when you are involving all three sides of the triangle. For a side – you know 2 sides (with the angle in between) and want to know the 3rd side. For an angle – you know all 3 sides to start with. Example :– Find the length of side BC. a2 = b2 + c2 – 2bcCosA = 62 + 92 – 2 x 6 x 9 x Cos32 = 36 + 81 – 91.589 = 25.411 a = √25.411 = 5.04m So BC = 5.04m Example :- Find the size of angle A. Cos A = 𝑏2 + 𝑐 2 − 𝑎2 2𝑏𝑐 = 52 + 62 − 42 2 ×5 ×6 45 = 60 = 0.75 A = Cos-1 0.75 = 41.4o = 25+36−16 60