The two sides of the triangle are 6 cm and 12 cm and the included angle is 60°. what's the measure of the third side.
a. 6.7
b. 8.5
c. 10.4
d. 12 5

C. 10,4

Step-by-step explanation:

Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.

Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:

c² = 36 + 144 - 144 cos 60°; 108 = c²

The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.

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**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.

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