Law of Sines and Triangle Properties

This video tutorial introduces the Law of Sines, explaining its application in solving oblique triangles. It outlines the conditions required to use the Law of Sines, such as angle-angle-side and angle-side-angle configurations. The video derives the Law of Sines using right triangles and demonstrates its use through an example problem. The tutorial concludes with a brief mention of further resources for learning about the Law of Sines and related topics.

What type of triangle is specifically addressed by the Law of Sines?

• Oblique triangle

• Equilateral triangle

• Isosceles triangle

• Right triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following is a requirement for using the Law of Sines?

• All sides are known

• Two sides and the included angle are known

• One side and two angles are known

• All angles are known

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the Law of Sines formula used for?

• Finding the area of a triangle

• Calculating the perimeter of a triangle

• Determining if a triangle is right-angled

• Solving for unknown sides or angles in a triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In the Law of Sines, what remains constant for any triangle?

• The length of the hypotenuse

• The sum of the angles

• The ratio of the sine of an angle to its opposite side

• The area of the triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How is the Law of Sines derived?

• By constructing altitudes and forming right triangles

• By using the cosine rule

• By using the Pythagorean theorem

• By calculating the area of the triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first step in solving a triangle using the Law of Sines?

• Calculate the area of the triangle

• Identify a known angle and its opposite side

• Find the hypotenuse

• Use the cosine rule

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CCSS.8.G.A.5

In the example problem, what is the measure of angle C?

• 48 degrees

• 54 degrees

• 78 degrees

• 90 degrees

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CCSS.8.G.B.8

Why can't the Pythagorean theorem be used in the example problem?

• The sides are not known

• The triangle is not right-angled

• The triangle is equilateral

• The angles are not known

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CCSS.8.G.B.8

What is the length of side B in the example problem?

• 10.2 feet

• 12.5 feet

• 13.6 feet

• 16.5 feet

What is a good way to double-check your work when solving triangles?

• Recalculate the area

• Use a different formula

• Ensure the longest side is opposite the largest angle

• Check if all sides are equal