Law of Sine and Cosine

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be 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 expressed as: c² = a² + b² - 2ab*cos(C).

Front

When do 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).

Front

When do 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

Calculate the length of side AC if AB = 30, angle A = 60 degrees, and angle B = 50 degrees.

Back

AC = 27 (using the Law of Sines).

Front

Find the length of side AC if AB = 12, angle A = 30 degrees, and angle B = 60 degrees.

Back

AC = 14 (using the Law of Sines).

Front

What is the measure of angle A if side a = 10, side b = 14, and side c = 12?

Back

Angle A = 78 degrees (using the Law of Cosines).

Front

What is the formula for the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

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

Back

The ratio of each side to the sine of its opposite angle is constant, meaning a/sin(A) = b/sin(B) = c/sin(C).

Front

How do you derive the Law of Cosines from the Pythagorean theorem?

Back

By extending one side of the triangle and applying the Pythagorean theorem to the resulting right triangle.