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# Law of Cosines: Difficult Problems with Solutions

Problem 1
Given a triangle ABC with AC=13, BC=18 and $$\angle ACB = 60^\circ$$, find the value of AB2 = ?.
Problem 2
In a triangle ABC, AC=12, BC=13, AB=14. Find $$\cos(\angle ACB)$$. In the answer box, write the fraction as a/b. If it is negative, write "-" directly before the fraction.
Problem 3
In a triangle ABC, AC=7, BC=15, AB=18. Find $$\cos(\angle ACB)$$. In the answer box, write the fraction as a/b. If it is negative, write "-" directly before the fraction.
Problem 4
In a triangle ABC, AC=14, BC=17, AB=20. Find $$\cos(\angle ACB)$$. In the answer box, write the fraction as a/b. If it is negative, write "-" directly before the fraction.
Problem 5
In a triangle ABC, AC=13, BC=16, AB=21. Find $$\cos(\angle ACB)$$. In the answer box, write the fraction as a/b. If it is negative, write "-" directly before the fraction.
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