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Contents 11.2 Sine Formula 11.3 Cosine Formula 11.4 Applications in Two-dimensional Problems 11.1 Area of Triangles 11 Trigonometry (2) Home

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Trigonometry (2) 11 Home Content P. 2 A. Area Formula of Triangles 11.1 Area of Triangles In Fig. 11.6, we take BC as the base and AD as the height of the triangle. Substituting h = b sin C into (*), we have Fig. 11.6

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Trigonometry (2) 11 Home Content P. 3 B. Heron’s Formula 11.1 Area of Triangles Another important formula for calculating the area of a triangle is Heron’s formula. Heron’s Formula For any triangles with the length of all the three sides known, Heron’s formula can be used to calculate its area.

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Trigonometry (2) 11 Home Content P Sine Formula or The Sine Formula states that: For any triangle, the length of a side is directly proportional to the sine of its opposite angle. Or mathematically, the sine formula can be expresses as:

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Trigonometry (2) 11 Home Content P. 5 A. Solving a Triangle with Two Angles and Any Side Given 11.2 Sine Formula 1.If any two angles ( A and B ) of a triangle and a side ( a ) opposite to one of the angles are given, we can use the sine formula directly to find b : 2.If any two angles ( A and B ) of a triangle are given, but the given side c is not an opposite side, we should find the third angle ( C ) first, then we can use the sine formula: Fig

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Trigonometry (2) 11 Home Content P. 6 B. Solving a Triangle with Two Sides and One Non-included Angle Given 11.2 Sine Formula Example 11.5T In ABC, a = 16 cm, b = 14 cm and B = 48 . (a) Find the possible values of A. (b) How many triangles can be formed? (a) By sine formula, (b) Two triangles can be formed. Solution:

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Trigonometry (2) 11 Home Content P Cosine Formula Notes: The following formulas are known as the cosine formulas: Cosine Formulas So Pythagoras’ Theorem is a special case of cosine formula for right-angled triangles.

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Trigonometry (2) 11 Home Content P. 8 A. Angle of Elevation and Angle of Depression 11.4 Applications in Two-dimensional Problems When we observe an object above us, the angle between our line of sight and the horizontal is called the angle of elevation (see Fig (a)). When we observe an object below us, the angle between the line of sight and the horizontal is called the angle of depression (see Fig (b)). Fig (a) Fig (b)

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Trigonometry (2) 11 Home Content P. 9 B. Bearing 11.4 Applications in Two-dimensional Problems (a) The compass bearing of A from O is N30 E. (b) The compass bearing of B from O is S40 W. When using compass bearing, all angles are measured from north (N) or South (S), thus the bearing is represented in the form Fig (a)

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Trigonometry (2) 11 Home Content P. 10 B. Bearing 11.4 Applications in Two-dimensional Problems (a) The bearing of C from O is 050 . For example, in Fig (b), O, C and D lie on the same plane. (b) The bearing of D from O is 210 . When using true bearing, all angles are measured from the north in a clockwise direction. The bearing is expressed in the form , where 0 < 360 . Fig (b)

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