Law of Cosine

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What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab cos(C), where c is the side opposite angle C.

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What is the formula for the Law of Cosines?

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c² = a² + b² - 2ab cos(C)

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How do you find the length of a side using the Law of Cosines?

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To find the length of a side, rearrange the Law of Cosines formula to solve for the desired side.

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What is the relationship between the sides and angles in a triangle according to the Law of Cosines?

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The Law of Cosines shows that the square of the length of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.

Front

How can the Law of Cosines be used to find an angle in a triangle?

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To find an angle, rearrange the Law of Cosines formula to isolate the cosine of the angle, then use the inverse cosine function.

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If a triangle has sides of lengths 7, 8, and 9, how can you find the angle opposite the side of length 9?

Back

Use the Law of Cosines: cos(C) = (a² + b² - c²) / (2ab), where a = 7, b = 8, and c = 9.

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What is the significance of the cosine function in the Law of Cosines?

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The cosine function relates the angle of the triangle to the lengths of the sides, allowing for the calculation of unknown angles or sides.

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What is the first step in applying the Law of Cosines to a triangle?

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Identify the lengths of the sides and the angle you want to find or the side you want to calculate.

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Can the Law of Cosines be used for non-right triangles?

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Yes, the Law of Cosines is applicable to all types of triangles, not just right triangles.

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What is the Law of Cosines used for in real-world applications?

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It is used in various fields such as engineering, physics, and computer graphics to calculate distances and angles.