Solving Story Problems with Law of Sines and Cosines

The video tutorial covers the application of the laws of sine and cosine in solving geometric problems. It begins with an introduction to when each law should be used, followed by two story problems. The first problem involves calculating the distance of a ship from a point on the shore using the law of sines. The second problem involves determining the distance between two boats using the law of cosines. The tutorial emphasizes understanding the arrangement of angles and sides in triangles to choose the appropriate law.

Which trigonometric law is used when you have two sides and the included angle of a triangle?

• Pythagorean Theorem

• Law of Cosines

• Law of Sines

• Tangent Law

What type of triangle scenario requires the use of the Law of Sines?

• SAS condition

• ASA condition

• SSS condition

• SSA condition

How far apart are James and Raul standing from each other?

• 15 miles

• 10 miles

• 20 miles

• 25 miles

What is the angle between the coastline and the line from the ship to James?

• 30 degrees

• 45 degrees

• 50 degrees

• 35 degrees

What is the missing side length from James to the ship calculated using the Law of Sines?

• 7.2 miles

• 9.0 miles

• 8.5 miles

• 6.5 miles

What is the angle opposite to the side we are trying to find in the problem involving James, Raul, and the ship?

• 100 degrees

• 45 degrees

• 90 degrees

• 35 degrees

What type of triangle configuration is used in the problem with the three boats at sea?

• ASA

• SAS

• SSA

• AAS

What law is applied to find the distance between J2 and J3?

• Law of Sines

• Sine Rule

• Pythagorean Theorem

• Law of Cosines

What is the distance between J2 and J3 calculated using the Law of Cosines?

• 2.9 miles

• 3.5 miles

• 3.0 miles

• 2.5 miles

Which angle is included between the sides in the triangle problem involving the three boats?

• 40 degrees

• 45 degrees

• 35 degrees

• 50 degrees