Law of Cosines

Front

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 angle opposite side c.

Front

When is the Law of Cosines used?

Back

The Law of Cosines is used to find a side or an angle in any triangle, especially when the triangle is not a right triangle.

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab * cos(C) where c is the side opposite angle C, and a and b are the other two sides.

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How do you find an angle using the Law of Cosines?

Back

To find an angle, rearrange the Law of Cosines formula to solve for cos(C): cos(C) = (a² + b² - c²) / (2ab). Then use the inverse cosine function.

Front

What does 'c' represent in the Law of Cosines?

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'c' represents the length of the side opposite the angle being calculated.

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What does 'a' and 'b' represent in the Law of Cosines?

Back

'a' and 'b' represent the lengths of the other two sides of the triangle.

Front

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) = (7² + 8² - 9²) / (2 * 7 * 8). Calculate to find angle C.

Front

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

Back

The Law of Cosines shows that the square of a side length 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 applied to find a missing side?

Back

Rearrange the Law of Cosines formula to solve for the missing side. For example, to find side c: c = √(a² + b² - 2ab * cos(C)).

Front

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

Back

The cosine function relates the angle to the lengths of the sides, allowing for the calculation of angles and sides in non-right triangles.