Exploring the Law of Sines in Oblique Triangles

Professor Dave introduces the law of sines, a trigonometric principle used to solve oblique triangles, which do not have a right angle. The video explains how to apply the law of sines to different triangle scenarios: side angle angle (SAA), angle side angle (ASA), and side side angle (SSA). It also covers potential issues with SSA, such as non-existent triangles or multiple solutions. Finally, the video presents a formula for calculating the area of oblique triangles using the sine of an angle between two sides.

What type of triangles does the law of sines apply to?

• Isosceles triangles

• Equilateral triangles

• Oblique triangles

• Right triangles

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What is the relationship between the sides and angles in the law of sines?

• Side A over sine A equals Side B over sine B

• Side A times sine A equals Side B times sine B

• Side A minus sine A equals Side B minus sine B

• Side A plus sine A equals Side B plus sine B

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CCSS.HSG.SRT.D.10

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How can you find the third angle in a triangle if two angles are known?

• Add the two angles and divide by two

• Subtract the two angles from 90

• Subtract the sum of the two angles from 180

• Multiply the two angles

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In a Side Angle Angle scenario, how do you find the unknown sides?

• Using Pythagoras' theorem

• Dividing the known side by the cosine of the known angle

• Multiplying the known side by sine of the known angle

• Applying the law of sines

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What is the significance of the side in an Angle Side Angle scenario?

• It has no significance

• It is the longest side of the triangle

• It is the shortest side of the triangle

• It is specifically the side between the two known angles

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In which scenario might you first need to find an angle opposite a known side length?

• Angle Angle Side

• Side Angle Angle

• Angle Side Angle

• Side Side Angle

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What can cause a triangle to not exist in a Side Side Angle scenario?

• If the sine of an angle exceeds one

• If the angles do not add up to 180 degrees

• If the sum of the sides is less than the third side

• If the cosine of an angle is negative

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How can the law of sines result in two solutions in a Side Side Angle scenario?

• If the sine of an angle could correspond to two different angles

• If the sine of an angle is one

• If the cosine of an angle could correspond to two different angles

• If the sine of an angle is zero

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CCSS.HSG.SRT.D.10

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What formula is used to calculate the area of an oblique triangle?

• One half base times height

• Product of the lengths of two sides and the sine of the angle between them

• Sum of all sides divided by the sine of the largest angle

• Product of the longest side and the sine of the opposite angle

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CCSS.HSG.SRT.D.9

How many ways can you calculate the area of an oblique triangle using the law of sines?

• Four

• Three

• Two

• One

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CCSS.HSG.SRT.D.11