95% of Students Make This Mistake With Law of COSINES

The video tutorial highlights common mistakes students make when using the law of cosines, especially regarding the ambiguous case. It provides an example problem, demonstrating how to correctly apply the law of cosines and avoid errors by not relying solely on the law of sines. The tutorial emphasizes the importance of understanding the problem setup and using the correct formulas to find missing angles in a triangle.

What is a common misconception students have when using the Law of Cosines?

• It always results in an obtuse angle.

• It eliminates the need to consider the ambiguous case.

• It requires the use of a scientific calculator.

• It is only applicable to right triangles.

In the given example, what is the first step to solve the triangle using the Law of Cosines?

• Directly solve for angle B.

• Use the Law of Sines to find an angle.

• Draw an oblique triangle to understand its shape.

• Calculate the area of the triangle.

Why is it important to be cautious when using the Law of Sines in ambiguous cases?

• It always results in acute angles.

• It can lead to incorrect obtuse angles.

• It requires more complex calculations.

• It is not applicable to any triangle.

What is the recommended method to avoid errors when dealing with side-angle-side scenarios?

• Use the Law of Cosines twice.

• Estimate the angles visually.

• Rely on a calculator's automatic functions.

• Use the Law of Sines twice.

What is the final step in solving the triangle after using the Law of Cosines?

• Subtract the known angles from 180 degrees.

• Re-draw the triangle for accuracy.

• Verify the results using the Law of Sines.

• Calculate the perimeter of the triangle.

What is the main advantage of using the Law of Cosines over the Law of Sines in ambiguous cases?

• It is faster to compute.

• It always provides the correct angle.

• It is applicable to all types of triangles.

• It requires fewer calculations.

What should you do if you encounter an ambiguous case while solving a triangle?

• Use the Law of Sines and assume an acute angle.

• Use a different mathematical method entirely.

• Guess the angle based on the triangle's appearance.

• Use the Law of Cosines to find one angle, then subtract from 180.