Law of Sines and Law of 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.

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, expressed as 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

How many triangles can be formed with A=53, b=6, and a=7?

Back

1 triangle can be formed.

Front

How many triangles can be formed with A=53, b=6, and a=4?

Back

0 triangles can be formed.

Front

How many triangles can be formed with A=53, b=6, and a=5?

Back

2 triangles can be formed.

Front

What is the ambiguous case in triangle problems?

Back

The ambiguous case occurs in SSA situations where two different triangles may be possible, one triangle, or no triangle at all.

Front

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

Back

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

Front

What does it mean if the Law of Sines gives a negative value for a side length?

Back

A negative value indicates that the triangle cannot be formed with the given dimensions.