Law of Sines and Cosines L

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What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in the triangle. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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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 useful for finding a side when two sides and the included angle are known, and is expressed as: c² = a² + b² - 2ab*cos(C).

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When would you use the Law of Sines instead of the Law of Cosines?

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The Law of Sines is typically used when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA). The Law of Cosines is used when you have two sides and the included angle (SAS) or all three sides (SSS).

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

Back

To find the length of a side using the Law of Cosines, rearrange the formula c² = a² + b² - 2ab*cos(C) to solve for the desired side. For example, to find side c, take the square root of (a² + b² - 2ab*cos(C)).

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

Back

According to the Law of Sines, the ratio of each side of a triangle to the sine of its opposite angle is equal. This means that larger angles correspond to longer sides and smaller angles correspond to shorter sides.

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How can you determine if a triangle is solvable with the given information?

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A triangle is solvable if you have enough information to apply either the Law of Sines or the Law of Cosines. This typically means having at least two sides and one angle, or two angles and one side.

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What is the formula for the Law of Sines?

Back

The formula for the Law of Sines is: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides opposite angles A, B, and C respectively.

Front

What is the formula for the Law of Cosines?

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The formula for the Law of Cosines is: 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 apply the Law of Sines to find an unknown angle?

Back

To find an unknown angle using the Law of Sines, rearrange the formula to isolate the sine of the angle. For example, sin(A) = a*sin(B)/b, then use the inverse sine function to find the angle A.

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What is the significance of the included angle in the Law of Cosines?

Back

The included angle is significant in the Law of Cosines because it is the angle between the two known sides. It is necessary for calculating the length of the third side.