Laws of Sine and Cosine

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 of 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 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

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

Back

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

Front

How do you find an unknown side using the Law of Cosines?

Back

To find an unknown side using the Law of Cosines, rearrange the formula: c² = a² + b² - 2ab*cos(C). Solve for the side by taking the square root after calculating the right side.

Front

What is the sum of angles in a triangle?

Back

The sum of the interior angles in a triangle is always 180 degrees.

Front

What is an ambiguous case in triangle solving?

Back

An ambiguous case occurs in the SSA condition where two different triangles can be formed from the given information.

Front

If angle A = 70° and angle B = 50.1°, what is angle C?

Back

Angle C = 180° - (A + B) = 180° - (70° + 50.1°) = 59.9°.

Front

Given sides a = 38, b = 31, c = 35, how do you find angles A, B, and C?

Back

Use the Law of Cosines to find one angle, then use the Law of Sines to find the others.