In order to apply the law of cosines to find the length of the side of a triangle, it is enough to know which of the following?A.The lengths of two of the triangle's sides and the measure of the angle between themB.At least two of the angles of the triangle and the length of one of its sidesC.The area of the triangle
Question
In order to apply the law of cosines to find the length of the side of a triangle, it is enough to know which of the following?A.The lengths of two of the triangle's sides and the measure of the angle between themB.At least two of the angles of the triangle and the length of one of its sidesC.The area of the triangle
Solution
The correct answer is A. The lengths of two of the triangle's sides and the measure of the angle between them.
The law of cosines, c² = a² + b² - 2ab*cos(C), is used to find the length of an unknown side of a triangle (c), given the lengths of the other two sides (a and b) and the cosine of the angle (C) between them.
Option B is not sufficient because knowing two angles of a triangle and the length of one side does not allow you to apply the law of cosines. You need to know the length of two sides and the included angle.
Option C is also not sufficient because the area of the triangle does not provide enough information to apply the law of cosines. You still need to know the lengths of two sides and the included angle.
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