Deriving the Law of Sines in Trigonometry

The video tutorial explains the derivation of the Law of Sines, a formula used to find missing sides or angles in any triangle. It begins by introducing the formula and setting up a triangle with labeled sides and angles. The instructor then drops an altitude to create right triangles, using trigonometric ratios to derive the formula. Through cross multiplication and simplification, the Law of Sines is established. The video concludes by explaining how the third side can be incorporated into the formula.

What is the Law of Sines used for?

• To calculate the perimeter of a triangle

• To calculate the area of a triangle

• To find missing sides or angles of any triangle

• To prove triangles are congruent

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Why are the variables a, b, and c used in lowercase for sides of the triangle?

• To represent angles

• Because they are constants

• To differentiate from the angles

• To indicate they are variables

What does dropping an altitude in a triangle help to create?

• Isosceles triangles

• Right triangles

• Equilateral triangles

• Scalene triangles

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What variable is used to represent the altitude in the derivation?

• a

• c

• h

• b

What does the variable 'h' stand for in the context of the derivation?

• Hypotenuse

• Harmonic mean

• Height

• Horizontal length

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CCSS.8.G.B.8

In the derivation, what is the ratio of the sine of angle A?

• h over b

• a over h

• h over a

• b over h

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CCSS.HSG.SRT.C.6

What operation is performed to solve for 'h' in both right triangles?

• Cross multiplication

• Addition

• Subtraction

• Multiplication

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CCSS.8.G.B.8

What does setting the two expressions equal to 'h' allow us to derive?

• The Law of Cosines

• The Law of Tangents

• The Law of Sines

• The Pythagorean theorem

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the final step in deriving the Law of Sines?

• Subtracting a and b from both sides

• Multiplying both sides by a and b

• Dividing both sides by a and b

• Adding a and b to both sides

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CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

How can the third angle be incorporated into the Law of Sines formula?

• By repeating the process with angle C

• By multiplying both sides by c

• By dropping an altitude from angle C

• By using the Pythagorean theorem

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11