Law of Cosines

The video tutorial explains how to solve a problem involving two boats traveling at different speeds and forming a 110-degree angle. The goal is to find the distance between the boats after 30 minutes. The instructor discusses the use of vectors and triangles, ultimately deciding to apply the law of cosines. The problem is broken down into steps, including converting speeds to distances for 30 minutes and performing calculations using the law of cosines. The instructor emphasizes the importance of ensuring the calculator is set to degrees and verifies the solution through calculations.

What is the angle formed between the courses of the two boats?

• 110 degrees

• 90 degrees

• 100 degrees

• 120 degrees

If a boat travels at 24 mph, how far does it travel in 30 minutes?

• 12 miles

• 8 miles

• 24 miles

• 16 miles

Which mathematical method is used to find the distance between the two boats?

• Law of sines

• Vector addition

• Pythagorean theorem

• Law of cosines

What is the formula for the law of cosines?

• a^2 = b^2 + c^2 - 2bc cos(A)

• c^2 = a^2 + b^2 - 2ab cos(C)

• b^2 = a^2 + c^2 - 2ac cos(B)

• c^2 = a^2 + b^2 + 2ab cos(C)

Why is it important to ensure the calculator is in the correct mode?

• To avoid syntax errors

• To ensure the correct angle measurement is used

• To save battery life

• To prevent overheating

What is the final calculated distance between the two boats?

• 23 miles

• 81 miles

• 12 miles

• 16 miles

What should you do if you make a mistake while entering data into the calculator?

• Ignore it and continue

• Use a different formula

• Switch to a different calculator

• Re-enter the data carefully