Transcript 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..

(e) cos 40°=0.766..
(f) cos 140°=-0.766..

(c) cos 10°=0.984..
(d) cos 170°=-0.984..


Note that the sine of an acute angle and its
(obtuse) supplement are the same.


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).



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.

Find the value of θ to the nearest degree if it
is obtuse.

Find the value of θ to the nearest degree if it
is obtuse.
10 m
22°
5m
θ

Find the value of θ to the nearest degree if it
is obtuse.
sin  sin 22o

10
5
10sin 22o
sin  
5
o 

10sin22
  sin1

5


  48.522222....
10 m
22°
5m
θ


Find the value of θ to the nearest degree if it is
obtuse.
sin  sin 22o

10
5
10sin 22o
sin  
5
o 

1 10sin22
  sin 

5


  48.522222....



10 m
22°
But θ is obtuse.
Therefore θ = 180 – 48.52222..
≈ 131°
5m
θ