Select the angle that correctly completes the law of cosines for this triangle.52 + 132 – 2(5)(13)cos ___ = 122A.90°B.67°C.180°D.23°
Question
Select the angle that correctly completes the law of cosines for this triangle.52 + 132 – 2(5)(13)cos ___ = 122A.90°B.67°C.180°D.23°
Solution
The Law of Cosines is used to find the angle in a triangle when we know the lengths of all three sides. The formula is c² = a² + b² - 2abcosC, where a, b, and c are the sides of the triangle, and C is the angle we are trying to find.
In this case, we have:
122 = 52 + 132 - 2(5)(13)cosC
We can see that the sides a and b are 5 and 13, and side c is 12. Therefore, we are solving for angle C.
So, the angle that correctly completes the law of cosines for this triangle is C.
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