5.4 the cosine law
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5.4 The Cosine Law
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April 24, 2013
5.4 The Cosine Law
Sine Law is the relationship between the sides and the sine of the opposite angles in a relationship.
The cosine law describes the relationship between the cosine of an angle and the lengths of the three sides of any triangle.
5.4 The Cosine Law
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For any triangle ABC, where a, b, and, c are the lengths of the sides opposite to ∠A, ∠B, ∠C respectively, the cosine law states that:
5.4 The Cosine Law
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Example 1. A surveyor needs to find the length of a swampy area near Fishing Lake, Manitoba. The surveyor sets up her transit at a point A. She measures the distance to one end of the swamp as 468.2 m, the distance tot he opposite end of the swamp as 692.6 m, and the angle of sight between the two as 78.6°. Determine the length of the swampy area, to the nearest tenth of a metre.
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Example 2. Find ∠C
A
B
C
14 19
12.2
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You can use sine law and cosine law in conjunction (i.e. together).Example 3: Solve the triangle.
A
BC
20°
11
5
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It is generally recommended that you use cosine law when dealing with angles.
Cosine law can deal with positive/negative values
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Homeworkp119#14, 10