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 2accosB x 2 = 4 2 + 7 2 2( 4 )( 7 )cos 50 x 2 =16+4956( 0.6428 ) x 2 =6535.997 x 2 =29.003 x=5.385 cm

(B) If you know 3 sides Þ Cosine rule

Example:

Calculate ÐBAC for the triangle above.
Solution:
cosA= b 2 + c 2 a 2 2bc cosBAC= 7 2 + 6 2 8 2 2(7)(6) cosBAC=0.25 BAC= cos 1 0.25 BAC= 75.52 o