Triangle Laws: Sine and Cosine

The video tutorial by Brandon Gley, a high school math teacher, explains the sine and cosine laws used to solve parts of a triangle. The sine law is useful when three out of four pieces of information from two ratios are known, while the cosine law is applicable when three sides and one angle are known. The tutorial provides examples to illustrate when to use each law, emphasizing the importance of knowing the right pieces of information. The video concludes with a summary of the four different situations where these laws can be applied.

What is the sine law used for in triangle calculations?

• To determine the type of triangle

• To calculate the perimeter of a triangle

• To solve for unknown sides or angles when two angles and one side are known

• To find the area of a triangle

Which of the following is a requirement for using the sine law?

• Knowing two sides and the angle between them

• Knowing two angles and any side

• Knowing all three sides of the triangle

• Knowing the area of the triangle

What is the cosine law used for in triangle calculations?

• To find the area of a triangle

• To solve for unknown sides or angles when three sides are known

• To calculate the perimeter of a triangle

• To determine the type of triangle

Which scenario is suitable for using the cosine law?

• When two angles and a side are known

• When three sides are known

• When two sides and an angle not between them are known

• When the area of the triangle is known

In a triangle with sides a, b, and c, and angle A, which formula represents the cosine law?

• a^2 = b^2 + c^2 - 2bc sin(A)

• a^2 = b^2 + c^2 - 2bc cos(A)

• a^2 = b^2 + c^2 + 2bc cos(A)

• a^2 = b^2 - c^2 + 2bc cos(A)

In the example with triangle DF, why is the sine law applicable?

• Because two sides and an angle not between them are known

• Because all three sides are known

• Because the area of the triangle is known

• Because two sides and the angle between them are known

In triangle GHJ, why can't the cosine law be used?

• Because only one side is known

• Because the area of the triangle is known

• Because all three sides are known

• Because two sides and an angle between them are known

In triangle KLM, which law is applicable and why?

• Sine law, because two sides and an angle not between them are known

• Cosine law, because two sides and the angle between them are known

• Cosine law, because all three sides are known

• Sine law, because two angles and a side are known

What is a key advantage of using the cosine law first in a problem?

• It allows for the use of the sine law afterwards

• It simplifies the calculation of the area

• It determines the type of triangle

• It calculates the perimeter directly

What is the sum of angles in any triangle?

• 90 degrees

• 360 degrees

• 180 degrees

• 270 degrees