How to find all of the missing parts of a triangle by first using the law of cosines

The video tutorial explains how to handle triangle values and identify triangle types using the law of cosines. It covers the application of the law of cosines to solve triangles, addresses common calculation mistakes, and demonstrates the use of the law of sines while avoiding ambiguous cases. The tutorial emphasizes step-by-step problem-solving to minimize errors.

What is the primary reason for using the law of cosines instead of the law of sines in a side-angle-side (SAS) scenario?

• The law of cosines is always more accurate.

• The law of cosines is easier to calculate.

• The law of sines requires a known angle-side ratio.

• The law of sines is not applicable to any triangle.

How can the law of cosines formula be adapted for different triangles?

• By converting it to the law of sines.

• By using only one formula for all triangles.

• By swapping the positions of the sides and angles.

• By changing the angle to a right angle.

What is a common mistake students make when using the law of cosines?

• Forgetting to square the sides.

• Using the wrong angle in the formula.

• Subtracting terms incorrectly due to order of operations.

• Adding all terms together.

Why is it important to follow the order of operations when calculating with the law of cosines?

• To ensure the calculation is quick.

• To avoid incorrect subtraction of terms.

• To make the formula easier to remember.

• To use the law of sines instead.

What is the advantage of using the law of sines after finding a ratio with the law of cosines?

• It is faster and avoids the ambiguous case.

• It is more accurate than the law of cosines.

• It requires fewer calculations.

• It can solve any triangle without additional information.

How can the ambiguous case in the law of sines be avoided?

• By always using the law of cosines.

• By using a calculator.

• By choosing the larger angle first.

• By selecting the smaller angle to solve first.

What is the final step in solving a triangle using trigonometric laws?

• Drawing the triangle to scale.

• Rechecking all calculations.

• Finding the last angle using the sum of angles in a triangle.

• Using the law of sines again.

Why is it important to determine which angle is smaller when using the law of sines?

• To ensure the triangle is drawn correctly.

• To make calculations easier.

• To use the law of cosines instead.

• To avoid having two obtuse angles in a triangle.

What is the result of using the law of sines on the smaller angle?

• It confirms the triangle is right-angled.

• It ensures the angle is acute.

• It provides the exact side length.

• It avoids the ambiguous case.

What is the sum of angles in any triangle?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees