10.2 The Cosine Rule

10.2 The Cosine Rule



The cosine rule can be used when
(i) two sides and the included angle, or
(ii) three sides of a triangle are given.


(A) If you know 2 sides and 1 angle between them [included angle] Þ Cosine rule

Example:

Calculate the length of AC, x, in cm for the triangle above.
Solution:
b 2 = a 2 + c 2 2 a c cos B x 2 = 4 2 + 7 2 2 ( 4 ) ( 7 ) cos 50 x 2 = 16 + 49 56 ( 0.6428 ) x 2 = 65 35.997 x 2 = 29.003 x = 5.385  cm


(B) If you know 3 sides ÞCosine rule

Example:

Calculate ÐBAC for the triangle above.
Solution:
cos A = b 2 + c 2 a 2 2 b c cos B A C = 7 2 + 6 2 8 2 2 ( 7 ) ( 6 ) cos B A C = 0.25 B A C = cos 1 0.25 B A C = 75.52 o

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