Understanding Parallelograms and the Law of Cosines

The video tutorial explains how to determine the length of a diagonal in a parallelogram using the law of cosines. It begins by discussing the properties of parallelograms, such as supplementary adjacent angles and equal opposite sides. The tutorial then applies the law of cosines to calculate the diagonal length, ensuring the use of the correct angle and sides. The calculation is demonstrated using a calculator, and the final result is approximately 12.6 meters.

What is the sum of adjacent angles in a parallelogram?

• 180°

• 90°

• 270°

• 360°

If one angle in a parallelogram is 79°, what is the measure of its adjacent angle?

• 79°

• 101°

• 90°

• 180°

Which property of a parallelogram states that opposite sides are equal?

• Diagonals bisect each other

• Opposite sides are equal

• Opposite angles are equal

• Adjacent angles are equal

In the Law of Cosines, which side is opposite to angle A?

• Side D

• Side C

• Side B

• Side A

What is the formula for the Law of Cosines?

• a^2 = 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)

• a^2 = b^2 + c^2 - 2bc * sin(A)

What is the first step in applying the Law of Cosines to find the diagonal?

• Calculate the perimeter

• Determine the height

• Identify the known angle

• Find the area

Why is it important to check the calculator mode before calculating?

• To ensure it is in standard mode

• To ensure it is in radian mode

• To ensure it is in degree mode

• To ensure it is in scientific mode

What is the approximate value of x^2 calculated using the Law of Cosines?

• 200

• 250

• 100

• 158.3

What is the final length of the diagonal in the parallelogram?

• 13.8 M

• 10.5 M

• 11.3 M

• 12.6 M

What is the principal square root of 158.3?

• 15.6

• 12.6

• 13.6

• 14.6