Exploring the Law of Sines and Cosines Through Examples

This video tutorial covers the laws of sines and cosines, explaining when and how to use each law for solving non-right triangles. It provides examples for both laws, demonstrating how to find missing angles and sides. The video concludes with a brief mention of the ambiguous case in the law of sines, encouraging viewers to explore further.

When do we use the Law of Sines and Cosines?

• Only in right triangles

• Only with equilateral triangles

• When we have a 90-degree angle

• When we don't have a right triangle

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How many ways can the Law of Sines formula be written?

• Three

• Two

• One

• Four

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What do you need to solve a triangle using the Law of Sines?

• Two angles and one side

• Only one angle

• Two sides and one angle

• All three sides

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What is the first step in solving for an angle using the Law of Sines?

• Multiply both sides by the side opposite the unknown angle

• Divide both sides by the sine of the known angle

• Take the sine inverse of the known side

• Cross multiply

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How do you find a missing side using the Law of Sines?

• Multiply by the tangent of the known angle

• Cross multiply and solve for the unknown

• Use the sine inverse

• Divide by the cosine of the known angle

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What is unique about the Law of Cosines formula?

• It includes a subtraction term unlike the Pythagorean theorem

• It cannot solve for angles

• It is identical to the Pythagorean theorem

• It only works for acute triangles

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When must you use the Law of Cosines?

• Only with isosceles triangles

• With any type of triangle

• When you have two sides and an included angle

• When you have all three angles

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What is the first step in solving for a side using the Law of Cosines?

• Add the squares of two sides and subtract the product of two sides and the cosine of the included angle

• Subtract the product of two sides and the cosine of the included angle

• Take the square root of the sum of squares of two sides

• Square the lengths of all sides

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How do you solve for a missing angle using the Law of Cosines?

• Multiply the sides by the sine of the given angle

• Divide the opposite side by the cosine of the angle

• Use the cosine inverse of the known side

• Take the cosine inverse of the calculated value

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What potential outcomes are there when solving triangles with the Law of Sines?

• One triangle only

• No triangles

• One or two triangles

• Two triangles only

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