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Sine Rule – Finding an Obtuse Angle

Sine Rule – Finding an Obtuse Angle. Evaluate (a) sin 30° (b) sin 150° (c) sin 60° (d) sin 120° (e) cos 40° (f) cos 140° (c) cos 10° (d) cos 170°. Evaluate (a) sin 30°= 0.5 (b) sin 150°= 0.5 (c) sin 60°= 0.866.. (d) sin 120°= 0.866..

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Sine Rule – Finding an Obtuse Angle

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  1. Sine Rule – Finding an Obtuse Angle

  2. Evaluate • (a) sin 30° (b) sin 150° • (c) sin 60° (d) sin 120° • (e) cos 40° (f) cos 140° • (c) cos 10° (d) cos 170°

  3. Evaluate • (a) sin 30°= 0.5 (b) sin 150°= 0.5 • (c) sin 60°= 0.866.. (d) sin 120°=0.866.. • (e) cos 40°=0.766.. (f) cos 140°=-0.766.. • (c) cos 10°=0.984.. (d) cos 170°=-0.984..

  4. Note that the sine of an acute angle and its (obtuse) supplement are the same.

  5. Note that the sine of an acute angle and its (obtuse) supplement are the same. • That means that any sine rule problem involving the missing angle could have two answers (an acute and obtuse).

  6. Note that the sine of an acute angle and its (obtuse) supplement are the same. • That means that any sine rule problem involving the missing angle could have two answers (an acute and obtuse). • In this course we assume the acute-angled answer, unless the obtuse angled answer is specifically requested.

  7. Example: • Find the value of θ to the nearest degree if it is obtuse.

  8. Example: • Find the value of θ to the nearest degree if it is obtuse. 10 m 5 m 22° θ

  9. Example: • Find the value of θ to the nearest degree if it is obtuse. 10 m 5 m 22° θ

  10. Example: • Find the value of θ to the nearest degree if it is obtuse. • But θ is obtuse. • Therefore θ = 180 – 48.52222.. • ≈ 131° 10 m 5 m 22° θ

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