Law of Sines and Law of Cosines

Which of the following formulas shows the Law of Cosines?

• c² = a² + b² - 4ac + cosA
• c² = a² - b² - 2abcosC
• c² = a² + b² - 2abcosC
• (cos A)/a = (cos B)/b

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Identify the Law of Sines

• Sin²x + Cos²x =1
• Sin(A)/a = Sin(B)/b = Sin(C)/c
• Sin(A)Sin(B)Sin(C) = 1
• Soh-Cah-Toa

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What are the possible criteria for the Law of Cosines?

• SSA, SSS

• SSA, ASA

• SSS, SAS

• AAS, ASA

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

• A

• B

• C

• D

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away, to 2 decimal places, is the bird from Amanda?

• 25.23 ft

• 23.19 ft

• 22.15 ft

• 20.85 ft

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Find m<B to the nearest whole number.

• A

• B

• C

• D

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Find the length of Side BC.

• 33

• 24

• 12

• 29

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Use the Law of Cosines to find the value of x.  (Level 1)

• 41.7
• 51.7
• 61.7
• 71.7

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49^o and Stake B measures an angle of elevation of 58^o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

• 152.7 feet

• 166.3 feet

• 157.3 feet

• 131.7 feet

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

When the measures of 2 angles of a triangle and the length of one of the non-included sides are given (AAS), to find either of the other 2 side lengths we use:

• Law of Sines

• Law of Cosines

• Law of Scones

• Law of Thermodynamics

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11