QZ-Law of Sines and Cosines

Front

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 is expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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

Front

When would you use the Law of Sines?

Back

The Law of Sines is used when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA) in a triangle.

Front

When would you use the Law of Cosines?

Back

The Law of Cosines is used when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Front

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

Back

To find the length of a side using the Law of Sines, you can rearrange the formula: a = b * (sin(A) / sin(B)), where A and B are the angles opposite sides a and b, respectively.

Front

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, you can use the formula: c = √(a² + b² - 2ab*cos(C)), where a and b are the lengths of the other two sides and C is the included angle.

Front

What is the relationship between the angles and sides in a triangle?

Back

In any triangle, the larger the angle, the longer the side opposite that angle. This relationship is fundamental in both the Law of Sines and the Law of Cosines.

Front

What is the sine of an angle in a right triangle?

Back

In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

How do you solve for an unknown angle using the Law of Sines?

Back

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