Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the law of sines, a mathematical principle used to solve non-right triangles. The instructor introduces the topic, explains the concept, and demonstrates its application through two example problems. The tutorial emphasizes the importance of understanding the law of sines for solving triangles and prepares students for an upcoming quiz. The video concludes with a reminder to review notes and practice the problems discussed.

What are the two topics discussed in Chapter 8?

• Pythagorean Theorem and Law of Tangents

• Law of Sines and Law of Cosines

• Vectors and Scalars

• Trigonometric Ratios and Circle Theorems

What is the formula for the Law of Sines?

• a^2 + b^2 = c^2

• a/b = sin(A)/sin(B)

• a^2 = b^2 + c^2 - 2bc*cos(A)

• sin(A)/a = sin(B)/b = sin(C)/c

How do you set up the equation using the Law of Sines to find side 'b'?

• b = a * sin(B)/sin(A)

• b/sin(B) = a/sin(A)

• b = sin(B) * a/sin(A)

• sin(B)/b = sin(A)/a

What is the correct setup to find the length of side BC in the triangle problem discussed?

• sin(93)/15 = sin(48)/BC

• BC = 15 * sin(48)/sin(93)

• sin(48)/15 = sin(93)/BC

• BC = sin(93) * 15/sin(48)

What is the next step after setting up the proportion in the Law of Sines?

• Subtract one side from the other

• Add the values together

• Divide both sides by the sine of the larger angle

• Cross multiply and solve for the unknown

How do you solve for angle 's' using the Law of Sines in the second problem?

• sin(120)/18 = sin(s)/11

• s = sin^-1(11 * sin(120)/18)

• s = 11 * sin(120)/18

• sin(s)/11 = sin(120)/18

What is the correct method to solve for 's' after setting up the equation?

• Multiply both sides by 18

• Subtract 18 from both sides

• Divide both sides by 18 and take the inverse sine

• Add 18 to both sides

What should you do if you make a mistake in your calculations?

• Start over from the beginning

• Check and correct the mistake quickly

• Ignore the mistake and continue

• Ask for help immediately

Why is it important to check if your answer is reasonable in triangle problems?

• To ensure the sides match the angles correctly

• To make sure the triangle is a right triangle

• To verify the triangle's area is correct

• To confirm the triangle's perimeter matches calculations

What is the significance of the angle size in relation to the side length it faces?

• Smaller angles face longer sides

• Larger angles always face shorter sides

• Larger angles face longer sides

• There is no relationship between angle size and side length