Maths: Analysis and Approaches · Geometry and trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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In a right-angled triangle, use the sine, cosine and tangent ratios and Pythagoras's theorem. In any other triangle, use the sine rule or the cosine rule. Side a is always opposite angle A, side b opposite angle B, and side c opposite angle C.
Choose the rule from what you are given. If you know a side and the angle opposite it, use the sine rule. If you know two sides and the angle between them, or all three sides, use the cosine rule.
In problems, draw a sketch first. Angles of elevation and depression are measured from the horizontal. A bearing is measured clockwise from north and written with three figures, such as 060°.
In the cosine rule students work out (a2 + b2 − 2ab) first and then multiply by cos C. Multiply 2ab by cos C first, then subtract the result from a2 + b2.
Answer: The third side is 13 cm.
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