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9.2 The Cosine Rule

9.2 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] ⇒ Cosine rule

Example:


Calculate the length of AC, x, in cm for the triangle above.

Solution:
b2=a2+c22accosBx2=42+722(4)(7)cos50x2=16+4956(0.6428)x2=6535.997x2=29.003x=5.385 cm

(B) If you know 3 sides ⇒ Cosine rule

Example:


Calculate ÐBAC for the triangle above.

Solution:
cosA=b2+c2a22bccosBAC=72+62822(7)(6)cosBAC=0.25BAC=cos10.25BAC=75.52o

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