12-5-24 (virtual) Law of Cosines

Front

What is the Law of Cosines?

Back

The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle.

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

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

Back

Rearrange the Law of Cosines formula to solve for the missing side, substituting known values for the other sides and the included angle.

Front

What is the first step in using the Law of Cosines to find an angle?

Back

Identify the lengths of all three sides of the triangle.

Front

If a triangle has sides of lengths 7, 8, and 9, how can you find the angle opposite the side of length 9?

Back

Use the Law of Cosines: cos(C) = (a² + b² - c²) / (2ab), where a = 7, b = 8, and c = 9.

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 cosine of the right angle is zero, simplifying the Law of Cosines to the Pythagorean theorem.

Front

How can the Law of Cosines be used in real-world applications?

Back

It can be used in fields such as engineering, navigation, and physics to calculate distances and angles in non-right triangles.

Front

What is the significance of the cosine function in the Law of Cosines?

Back

The cosine function relates the angle of the triangle to the lengths of its sides, allowing for the calculation of unknown angles or sides.

Front

What is the angle of a triangle if the sides are 5, 12, and 13?

Back

The angle opposite the side of length 13 can be found using the Law of Cosines, which will yield 90 degrees, indicating a right triangle.

Front

How do you determine if a triangle is obtuse using the Law of Cosines?

Back

If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse.