Law of Sines and Cosines Concepts

The video tutorial covers the laws of sines and cosines, explaining their use in solving non-right triangles. It provides step-by-step examples of how to apply these laws to find missing sides and angles, emphasizing the importance of setting up correct proportions and using calculators for trigonometric calculations. The tutorial also highlights the specific cases where each law is most applicable.

What is the Law of Sines used for?

• Finding the area of a triangle

• Finding the perimeter of a triangle

• Finding missing sides and angles in non-right triangles

• Finding missing sides and angles in right triangles

Which of the following is a requirement to use the Law of Sines?

• Two angles and the included side

• Three sides

• Two sides and the included angle

• Two angles and the non-included side

In the proportion a/sin(A) = b/sin(B) = c/sin(C), what does 'a' represent?

• The included angle between sides b and c

• The angle opposite side A

• The hypotenuse of the triangle

• The side opposite angle A

When solving for a side using the Law of Sines, what is the first step after setting up the proportion?

• Add the angles together

• Cross multiply

• Divide by the sine of the angle

• Subtract the sides

What is the next step after cross-multiplying in the Law of Sines?

• Multiply the sides

• Divide both sides by the sine of the known angle

• Add the angles together

• Subtract the sides

What is the Law of Cosines used for?

• Finding the area of a triangle

• Finding missing sides and angles in non-right triangles

• Finding the perimeter of a triangle

• Finding missing sides and angles in right triangles

Which formula represents 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 sin(A)

• a^2 = b^2 + c^2 - 2bc cos(A)

When solving for a side using the Law of Cosines, what is the first step?

• Subtract the sides

• Add the angles together

• Square the known sides

• Multiply the sides by the cosine of the angle

What is the final step when solving for a side using the Law of Cosines?

• Multiply the sides

• Divide by the cosine of the angle

• Take the square root of both sides

• Add the angles together

When solving for an angle using the Law of Cosines, what must you do after isolating the cosine term?

• Add the angles together

• Multiply the sides by the cosine of the angle

• Take the inverse cosine of both sides

• Square the known sides