Sine Rule

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 1200.866..
• (e) cos 400.766.. (f) cos 140-0.766..
• (c) cos 100.984.. (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 ? to the nearest degree if it
  is obtuse.

8
Example

• Find the value of ? to the nearest degree if it
  is obtuse.

10 m
5 m
?
22
9
Example

• Find the value of ? to the nearest degree if it
  is obtuse.

10 m
5 m
?
22
10
Example

• Find the value of ? to the nearest degree if it
  is obtuse.
• But ? is obtuse.
• Therefore ? 180 48.52222..
• 131

10 m
5 m
?
22