Applying the law of cosines to a triangle to find the missing length

The video tutorial explains a geometry problem involving points on the shoreline of Lake George. The teacher guides through the process of analyzing the triangle formed by these points, discussing why certain formulas like the Pythagorean theorem and trigonometric functions are not applicable. The focus is on using the law of cosines to calculate the distance between two points, A and B, given the distances from a third point, C, and the angle at C. The tutorial concludes with the calculation of the distance, ensuring the result is reasonable within the context of the problem.

What are the given distances from point C to points A and B?

• 150 meters and 130 meters

• 180 meters and 120 meters

• 200 meters and 100 meters

• 160 meters and 140 meters

What is the measure of angle C given in the problem?

• 60.5 degrees

• 56.3 degrees

• 50.7 degrees

• 45.0 degrees

Why can't the Pythagorean theorem be applied to this problem?

• The triangle is isosceles

• The triangle is scalene

• The triangle is not a right triangle

• The triangle is equilateral

Why is the Law of Sines not applicable in this scenario?

• There is no known opposite side for the given angle

• The triangle is a right triangle

• The triangle is equilateral

• The triangle is isosceles

Which law is used to solve the problem of finding the distance between points A and B?

• Law of Tangents

• Pythagorean Theorem

• Law of Cosines

• Law of Sines

What is the formula for the Law of Cosines used in this problem?

• C^2 = A^2 + B^2 - 2AB * sin(C)

• C^2 = A^2 - B^2 - 2AB * cos(C)

• C^2 = A^2 + B^2 + 2AB * cos(C)

• C^2 = A^2 + B^2 - 2AB * cos(C)

What is the calculated distance between points A and B?

• 155.20 meters

• 145.30 meters

• 160.50 meters

• 151.10 meters