Sections:

Law of Sines and Law of Cosines, Page 12

Law of Cosines: Examples

Let’s go through a couple of examples using the Law of Cosines.

Example 1:

Given triangle ABC, with b = 8.5, c = 11.2, and A = 48.5°, solve the triangle (round to the nearest tenth).

As before, make sure to draw a diagram first. 

5.2.13 graphic 1

Find a:

a^2 = b^2 + c^2 - 2bc cos A; a^2 = (8.5)^2 + (11.2)^2 - 2(8.5)(11.2) cos48.5; a^2 = 197.7 - 126.2; a = 8.5
Find B:

b^2 = a^2 + c^2 - 2ac cos B; (8.5)^2 = (8.5)^2 + (11.2)^2 - 2(8.5)(11.2) cosB; 72.3 = 197.7 - 190.4 cosB; B = 48.8 degrees

Find C:

the measure of angle C = 180 - (48.8 + 48.5) = 82.7 degrees