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. Formula: 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 used to find a side or angle in a triangle when the Law of Sines cannot be applied. Formula: c² = a² + b² - 2ab*cos(C).

Front

When do you use the Law of Sines?

Back

Use the Law of Sines when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When do you use the Law of Cosines?

Back

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

Front

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).

Front

What is the formula for the Law of Cosines?

Back

The formula for the Law of Cosines is: c² = a² + b² - 2ab*cos(C).

Front

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

Back

To find an angle using the Law of Sines, rearrange the formula to sin(A) = a*sin(B)/b, then use the inverse sine function (sin⁻¹) to calculate the angle.

Front

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

Back

To find a side using the Law of Cosines, rearrange the formula to c = √(a² + b² - 2ab*cos(C)).

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

What is the significance of the Law of Sines in solving triangles?

Back

The Law of Sines is significant because it allows for the calculation of unknown angles and sides in non-right triangles, making it essential for solving various geometric problems.