Trigonometry and Distance Calculations

This video tutorial demonstrates how to solve an application problem using the Law of Cosines. It explains the relationship between the sides and angles of a triangle and how to apply the Law of Cosines to determine the length of a side. The tutorial provides a step-by-step calculation of the side length using given measurements and concludes with the final result, which is the distance across a lake. The example is intended to help viewers understand the practical application of the Law of Cosines in solving real-world problems.

What mathematical concept is used to solve the problem of finding the distance across the lake?

• Law of Cosines

• Pythagorean Theorem

• Law of Sines

• Trigonometric Ratios

In the context of the Law of Cosines, what is always true about side 'A'?

• It is the longest side

• It is adjacent to angle 'A'

• It is opposite angle 'A'

• It forms angle 'A' with side 'B'

Which sides form angle 'A' in the triangle discussed?

• Sides A and C

• All three sides

• Sides B and C

• Sides A and B

What is the formula used to calculate X squared in the problem?

• X^2 = A^2 + B^2 - 2AB cos(C)

• X^2 = B^2 + C^2 - 2BC cos(A)

• X^2 = A^2 + C^2 - 2AC cos(B)

• X^2 = A^2 + B^2 + C^2

What is the value of the cosine of the angle used in the calculation?

• 60 degrees

• 45 degrees

• 30 degrees

• 36 degrees

What is the approximate value of X squared after evaluating the equation?

• 3.24

• 7.28

• 6.25

• 2.21

What is the purpose of ensuring the calculator is in degree mode?

• To avoid errors in multiplication

• To ensure the correct formula is used

• To simplify the calculation

• To match the angle measurement

What operation is performed to find the final distance across the lake?

• Subtraction

• Square root

• Multiplication

• Addition

What is the approximate distance across the lake in kilometers?

• 2.5 kilometers

• 1.8 kilometers

• 2.1 kilometers

• 1.5 kilometers

Why is only the positive square root considered in the final calculation?

• Because the triangle is isosceles

• Because the angle is acute

• Because the cosine is positive

• Because distance cannot be negative