10.1 The Sine Rule


(A) If you know 2 angles and 1 side ÞSine rule

Example:


Calculate the length, in cm, of AB.
Solution:
ÐACB = 180o – (50o + 70o) = 60o
A B sin 60 o = 4 sin 50 o A B = 4 × sin 60 o sin 50 o A B = 4.522  cm


(B) If you know 2 sides and 1 angle (but not between them) Þ Sine rule

Example:

Calculate ÐACB.
Solution:
28 sin 54 o = 26 sin A C B sin A C B = 26 × sin 54 o 28 sin A C B = 0.7512 A C B = 48.7 o


(C) Case of ambiguity (2 possible triangles)

Example

Calculate ÐACBθ.

Solution:
Two possible triangle with these measurement
AB = 26cm         BC = 28 cm           Ð BAC = 54o
26 sin θ = 28 sin 54 o sin θ = 0.7512 θ = sin 1 0.7512 θ = 48.7 o , 180 o 48.7 o θ = 48.7 o  (Acute angle) ,   131.3 o  (Obtuse angle)

Leave a Comment