Applications of the Law of Sines and Cosines

This video tutorial covers solving word problems using the laws of sines and cosines. It includes three examples: calculating the total distance of a boat race, determining the distance from a pitcher's mound to first base on a softball field, and finding the bearing of a ship's course. Each example demonstrates the application of trigonometric laws to solve real-world problems, emphasizing the importance of understanding angles and distances in various contexts.

What does the Law of Sines relate in a triangle?

• The ratio of each side length to the cosine of the opposite angle

• The product of side lengths and the sine of the included angle

• The ratio of each side length to the sine of the opposite angle

• The difference between side lengths and the sine of the opposite angle

What is required to use the Law of Cosines?

• Two sides and the included angle or three sides

• Only the three angles of the triangle

• At least one angle and all three sides

• Two angles and one side

In the boat race problem, what is the approximate length of side 'a'?

• 5.145 km

• 6.308 km

• 8 km

• 19.453 km

How is the total distance of the boat race calculated?

• Subtracting the shortest side from the sum of the other two

• Multiplying the longest side by two

• Adding the lengths of all sides

• Using the Pythagorean theorem

What is the distance from the pitcher's mound to first base in the softball field problem?

• 45 feet

• 43 feet

• 42.4 feet

• 60 feet

Which law is used to solve the softball field problem?

• None of the above

• Law of Sines

• Law of Cosines

• Pythagorean theorem

What type of triangle configuration is used in the ship navigation problem?

• Angle-Angle-Side

• Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

What is the bearing from point B to point C in the ship navigation problem?

• West 76.15 degrees South

• South 76.15 degrees West

• East 76.15 degrees North

• North 76.15 degrees East

How is the angle for the bearing calculated in the ship navigation problem?

• Adding 90 degrees to the calculated angle

• Subtracting 90 degrees from the calculated angle

• Multiplying the calculated angle by two

• Dividing the calculated angle by two

What is the correct expression for using the Law of Cosines to find a side in a triangle?

• a = sqrt(b^2 + c^2 - 2bc * cos(A))

• a = sqrt(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)