Law of Sines and Vectors

This video tutorial covers trigonometry concepts, including the Law of Sines and Cosines, and their applications in solving triangles and indirect measurement. It also introduces vectors, explaining their properties and uses. The tutorial provides examples and encourages students to practice solving problems using these mathematical principles.

What is the Law of Sines formula for any triangle?

• sin(A)/a = sin(B)/b = sin(C)/c

• a^2 + b^2 = c^2

• tan(A) = opposite/adjacent

• cos(A) = b/c

In the example given, what is the value of x when solving sin(60)/x = sin(78)/8?

• 7.08

• 8.07

• 6.08

• 9.08

What is the general form of the Law of Cosines?

• a^2 = b^2 + c^2 - 2bc cos(A)

• a^2 + b^2 = c^2

• cos(A) = b/c

• tan(A) = opposite/adjacent

In the example given, what is the value of a when solving 15^2 + 19^2 - 2(15)(19)cos(125)?

• 31.12

• 30.21

• 28.45

• 29.87

What is the angle A when solving 1.9^2 = 1.3^2 + 2.1^2 - 2(1.3)(2.1)cos(A)?

• 8.67 degrees

• 5.87 degrees

• 7.68 degrees

• 6.87 degrees

What is the height of the tree if it grows at a 78-degree angle and the angle to the top of the tree from 10 feet away is 61 degrees?

• 12.33 feet

• 15.33 feet

• 13.33 feet

• 14.33 feet

What does it mean to solve a triangle?

• Find all three angles and all three sides

• Find the height of the triangle

• Find the area of the triangle

• Find the perimeter of the triangle

What are the two characteristics of a vector?

• Magnitude and direction

• Angle and side

• Length and width

• Height and base

What is the resultant vector?

• The product of two vectors

• The quotient of two vectors

• The sum of two or more vectors

• The difference between two vectors

What method is used to find the resultant vector?

• Triangle method

• Parallelogram method

• Circle method

• Rectangle method