Law of Cosines

Front

What is the Law of Cosines?

Back

Front

What is the formula for finding the length of a side using the Law of Cosines?

Back

Front

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

Back

Front

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

Back

In any 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 Cosines in triangle calculations?

Back

The Law of Cosines is essential for solving triangles when you know two sides and the included angle or all three 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

Front

What is the cosine of 90 degrees?

Back

The cosine of 90 degrees is 0.

Front

What is the Law of Cosines used for in real-world applications?

Back

It is used in fields such as engineering, physics, and computer graphics to calculate distances and angles in non-right triangles.

Front

How can the Law of Cosines be derived from the Pythagorean theorem?

Back

The Law of Cosines generalizes the Pythagorean theorem for any triangle by incorporating the cosine of the angle between two sides.

Front

What is the relationship between the Law of Cosines and the Law of Sines?

Back

Both laws are used to solve triangles, but the Law of Sines is more applicable for cases with known angles, while the Law of Cosines is used for known sides.