Understanding the Law of Cosine

The video tutorial introduces the Law of Cosine, explaining its formula and when to use it. It covers two main scenarios: when all three sides of a triangle are known (SSS) and when two sides and the included angle are known (SAS). The tutorial provides detailed examples for both scenarios, demonstrating how to solve for unknown angles and sides using the Law of Cosine. It emphasizes the importance of starting with the largest angle and checking calculations carefully.

What is the basic formula for the Law of Cosine when solving for side 'a'?

• a² = b² + c² - 2bc sin(A)

• a² = b² - c² - 2bc cos(A)

• a² = b² + c² + 2bc cos(A)

• a² = b² + c² - 2bc cos(A)

In which scenario would you use the Law of Cosine?

• When you know all three angles of a triangle

• When you know two sides and the included angle

• When you know one side and two angles

• When you know the perimeter of the triangle

What is the first step in solving for an angle using the Law of Cosine?

• Add all sides together

• Multiply all sides together

• Subtract the known sides from the longest side

• Square the known sides and subtract from the longest side squared

When solving for angle B in Example 1, what is the value of cos(B) after calculations?

• -0.5509

• 0.4509

• 0.5509

• -0.4509

What is the next step after finding one angle in a triangle using the Law of Cosine?

• Find the perimeter of the triangle

• Calculate the area of the triangle

• Use the Law of Sine to find another angle

• Use the Law of Cosine again to find another angle

In Example 2, what is the first calculation step when given two sides and an included angle?

• Use the Law of Cosine to find the unknown side

• Calculate the area of the triangle

• Find the perimeter of the triangle

• Use the Law of Sine to find the third side

What is the calculated length of side 'a' in Example 2?

• 21.26

• 15.00

• 10.00

• 25.26

How do you find the remaining angles after calculating one angle using the Law of Cosine?

• Add all angles together

• Use the Pythagorean theorem

• Subtract from 180 degrees

• Use the Law of Sine

What is a key difference between side-side-side and side-angle-side scenarios?

• Side-side-side requires the Law of Sine

• Side-angle-side is easier because it doesn't require working backwards

• Side-side-side is used when angles are known

• Side-angle-side requires knowing all angles

What should you be cautious about when using the Law of Cosine?

• Forgetting to square the sides

• Using the wrong angle

• Incorrectly applying the triangle inequality theorem

• Misplacing the negative sign