Chapter 4: Non-right-angled Trigonometry Notes

Sections

1. 4A Right-angled trigonometry, elevation and depression Mastered

   A quick review of SOH CAH TOA, then angles of elevation and depression, eye height, and problems that use two right-angled triangles.

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2. 4B Compass and true bearings Mastered

   Writing directions as compass bearings and true bearings, converting between them, back bearings, and finding the angles inside a triangle formed by a two-leg trip.

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3. 4C Obtuse angles and the area of a triangle Mastered

   Sine, cosine and tangent of angles between 90° and 180°, why sin θ = sin(180° − θ), and the area formula A = ½ab sin C for any triangle.

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4. 4D The sine rule Mastered

   Labelling a triangle, the sine rule for finding a side or an angle, when to use it (a matching side and angle pair), and the obtuse-angle trap.

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5. 4E The cosine rule Mastered

   The cosine rule for a side (two sides and the included angle) and for an angle (three sides), how a negative cosine signals an obtuse angle, and choosing between the sine rule and the cosine rule.

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6. 4F Multi-step problems and radial surveys Mastered

   Problems that combine bearings with the sine and cosine rules, and compass radial surveys: finding the boundary lengths, perimeter and area of a block of land from bearings and distances measured from one central point.

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