How to find the missing lengths using law of cosines

The video tutorial explains the application of the law of cosines and the law of sines in solving triangle problems. It begins with an introduction to the cosine law formulas, followed by a detailed step-by-step application of these formulas to find side lengths and angles. The tutorial then transitions to using the law of sines for further angle calculations, concluding with final calculations and a summary of the problem-solving process.

What is the primary reason the law of sines cannot be used initially in this problem?

• The side lengths are not integers.

• The triangle is not drawn to scale.

• There is no known angle-side pair.

• The triangle is not a right triangle.

Which formula is used to find the side length 'a' using 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 * cos(A)

What is the calculated value of side 'a' after using the law of cosines?

• 8.64

• 9.64

• 7.64

• 6.64

After finding side 'a', what allows the use of the law of sines?

• The triangle becomes a right triangle.

• A known angle-side pair is established.

• The triangle is equilateral.

• All angles are now known.

What is the next step after finding side 'a' using the law of cosines?

• Calculate angle C using the law of cosines.

• Recalculate side 'a' for accuracy.

• Find the perimeter of the triangle.

• Use the law of sines to find angle B.

How is angle C determined after finding angles A and B?

• By using the Pythagorean theorem.

• By measuring directly with a protractor.

• By subtracting the sum of angles A and B from 180 degrees.

• Using the law of cosines again.

What is the final step in solving the triangle?

• Check if the triangle is isosceles.

• Calculate the area of the triangle.

• Draw the triangle to scale.

• Verify all calculations.