Trigonometry and the Law of Cosines

The video tutorial explains how to determine the steepness of a hill using trigonometry. It begins by measuring the dimensions of a triangular hill and then applies the law of cosines to calculate the angle of inclination, theta. The tutorial provides a detailed step-by-step solution, including calculations and simplifications, to find the angle using a calculator. The final result shows the angle of inclination, giving insight into the hill's steepness.

What is the length of the base of the triangle formed by the hill?

• 70 meters

• 20 meters

• 60 meters

• 50 meters

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which trigonometric law is suggested to find the angle of inclination?

• Pythagorean Theorem

• Law of Sines

• Law of Cosines

• Law of Tangents

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first step in applying the law of cosines to this problem?

• Identify the angle

• Identify the sides

• Calculate the area

• Use the Pythagorean theorem

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CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.10

In the law of cosines, what does the side 'C' represent?

• The longest side

• Any side

• The shortest side

• The side opposite the angle

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CCSS.6.EE.A.1

What is the value of 50 squared in the equation?

• 6,000

• 2,500

• 3,600

• 400

What is the simplified form of the cosine of theta in the equation?

• 3/4

• 19/20

• 57/60

• 1/2

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CCSS.HSG.SRT.C.8

What operation is performed to isolate the cosine of theta?

• Subtraction

• Addition

• Multiplication

• Division

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CCSS.6.EE.B.7

What is the result of subtracting 6,100 from both sides of the equation?

• 400

• 5,700

• 3,600

• 6,000

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CCSS.4.MD.C.6

What is the approximate angle of inclination of the hill in degrees?

• 22.3 degrees

• 15.7 degrees

• 20.5 degrees

• 18.2 degrees

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CCSS.HSF.TF.B.7

What mathematical function is used to find the angle from the cosine value?

• Inverse tangent

• Inverse secant

• Inverse sine

• Inverse cosine

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CCSS.HSF.TF.B.7