Understanding the Law of Cosines

This video tutorial explains the Law of Cosines, highlighting when it is necessary to use it over the Law of Sines. The instructor provides a detailed example, demonstrating how to solve a triangle when given two sides and the included angle, or all three sides. The process involves labeling the triangle, applying the Law of Cosines formula, and simplifying the equation to find the unknown side. The video concludes with a suggestion to use the Law of Sines for further solving, offering a link to a related video.

Why might the Law of Cosines be necessary when solving a triangle?

• It is used when the Law of Sines is not applicable.

• It is used to find the area of a triangle.

• It is used to calculate the perimeter of a triangle.

• It is used to determine the type of triangle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In which scenario would you apply the Law of Cosines?

• When given two sides and the included angle.

• When given two angles and a side.

• When given all three angles.

• When given one side and one angle.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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

• Determine the type of triangle.

• Find the perimeter of the triangle.

• Label the sides and angles of the triangle.

• Calculate the area of the triangle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which formula would you use if you are missing side B in a triangle?

• B squared = A squared + C squared + 2AC cos(B)

• A squared = B squared + C squared - 2BC cos(A)

• B squared = A squared + C squared - 2AC cos(B)

• C squared = A squared + B squared - 2AB cos(C)

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CCSS.8.G.B.8

What is the value of B squared after plugging in the known values?

• 225

• 144

• 86.1579

• 81

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CCSS.8.G.B.7

How do you find the length of side B after calculating B squared?

• Divide B squared by 2.

• Multiply B squared by 2.

• Take the square root of B squared.

• Add 10 to B squared.

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CCSS.8.G.B.8

What is the final length of side B rounded to one decimal point?

• 10.5 units

• 9.3 units

• 8.7 units

• 7.9 units

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What method is suggested for further solving the triangle after using the Law of Cosines?

• Heron's Formula

• Law of Sines

• Pythagorean Theorem

• Law of Tangents

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Why might the Law of Sines be preferred for further solving the triangle?

• It is more reliable.

• It is more accurate.

• It requires fewer calculations.

• It is quicker.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What should you do if you have questions after watching the video?

• Ignore the questions.

• Search for other videos.

• Leave a comment below the video.

• Rewatch the video.