Sine and Cosine Law Applications

The video tutorial covers the sine and cosine laws, explaining how to label triangles and apply these laws to solve for unknown angles and sides. It includes detailed examples of using the sine law to find missing angles and sides in triangles, as well as using the cosine law for side-angle-side combinations. The tutorial emphasizes the importance of understanding the relationships between angles and sides in triangles and provides step-by-step solutions to example problems.

What is the convention for labeling angles in a triangle?

• Symbols for angles

• Numbers for angles

• Lowercase letters for angles

• Uppercase letters for angles

In the Sine Law, what is the relationship between the sides and angles?

• sin a / A = sin b / B = sin c / C

• sin A / a = sin B / b = sin C / c

• a / sin A = b / sin B = c / sin C

• A / sin a = B / sin b = C / sin c

Which of the following is a requirement for using the Sine Law?

• All sides must be known

• All angles must be known

• The triangle must be right-angled

• A side must be opposite a known angle

What is a key difference between the Sine Law and the Cosine Law?

• Cosine Law can be used with all sides known

• Cosine Law is only for isosceles triangles

• Sine Law is used for equilateral triangles

• Sine Law requires a right triangle

When using the Cosine Law, what is typically memorized?

• Neither version

• The side version of the formula

• The angle version of the formula

• Both versions equally

In the example problem, what is the first step to find angle D using the Sine Law?

• Use the Cosine Law

• Find angle E first

• Calculate the length of side D

• Set up the ratio sin D / D = sin F / F

What is the value of angle D found in the example problem?

• 30 degrees

• 110 degrees

• 70 degrees

• 40 degrees

How is the unknown side x calculated in the example using the Sine Law?

• x = 3.3 * sin 70 / sin 40

• x = 3.3 * sin 110 / sin 30

• x = 3.3 * sin 30 / sin 110

• x = 3.3 * sin 40 / sin 70

In the Cosine Law example, what is the first step to find side Q?

• Use the formula q^2 = r^2 - p^2 - 2rp cos Q

• Use the formula q^2 = r^2 - p^2 + 2rp cos Q

• Use the formula q^2 = r^2 + p^2 + 2rp cos Q

• Use the formula q^2 = r^2 + p^2 - 2rp cos Q

What is the calculated length of side Q in the example problem?

• 6.2 meters

• 5 meters

• 7 meters

• 5.1 meters