Law of Cosines

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 other sides and angles are known.

Front

When is the Law of Cosines used?

Back

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

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab * cos(C), where c is the side opposite angle C, and a and b are the other two sides.

Front

If a triangle has sides of lengths 5, 6, and 7, how can you find the angle opposite the side of length 7?

Back

Use the Law of Cosines: cos(C) = (a² + b² - c²) / (2ab). Here, a=5, b=6, c=7.

Front

What does 'cos' represent in the Law of Cosines?

Back

'cos' represents the cosine function, which is a trigonometric function relating the angle of a triangle to the ratio of the lengths of the adjacent side to the hypotenuse.

Front

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

Back

Rearrange the Law of Cosines formula to solve for the unknown side.

Front

What is the relationship between the Law of Cosines and the Pythagorean theorem?

Back

The Law of Cosines generalizes the Pythagorean theorem. When the triangle is a right triangle, the Law of Cosines simplifies to the Pythagorean theorem.

Front

What is the significance of the angle in the Law of Cosines?

Back

The angle determines how the lengths of the sides relate to each other. It is crucial for calculating unknown sides or angles.

Front

Can the Law of Cosines be used for non-triangular shapes?

Back

No, the Law of Cosines is specifically applicable to triangles.

Front

What is the first step in using the Law of Cosines?

Back

Identify the known sides and the angle you want to find or the side you want to calculate.