Law of Sines and Ambiguous Case

In ΔABC, m∡B = 45°, a = 28 and b = 27. Find all possible values for m∡A.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Use the Law of Sines to solve for BC

• 33

• 24

• 12

• 29

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following sets of given information can be solved with the Law of Sines? Select all that apply

• Given: side a, angle B, angle C

• Given: side b, angle A, angle B

• Given: side a, side b, side c

• Given: side c, side a, angle B

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In this SSA - ambiguous case diagram, what happens if the length of side a is smaller than the value of h?

• No triangle can be formed.

• There will be two possible triangle solutions.

• A right triangle will be formed

• There will be one triangle formed, but it will not be a right triangle.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

For the SSA - two solution case, what are the values of angles B₁ and B₂? Given: angle A = 40^o, side a = 12, side b = 14

• angle B₁ = 48.6^o, angle B₂ = 131.4^o

• angle B₁ = 33.4^o, angle B₂ = 146.6^o

• angle B₁ = 48.6^o, angle B₂ = 41.4^o

• angle B₁ = 33.4^o, angle B₂ = 56.6^o

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

True/False: In order to use the Law of Sines, you must know a matching pair of angle & opposite side.

• True

• False

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

All of the following sets of given information can be solved with the Law of Sines except:

• Given: side a, side b, Angle C

• Given: side c, side a, angle C

• Given: angle A, angle B, side a

• Given: angle B, angle C, side a

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many solutions does the following SSA ambiguous case have? Given: angle A = 67o, side a = 17, side b = 20

• 0

• 1

• 2

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many solutions does the following SSA ambiguous case have?

Given: angle A = 32^o, side a = 7, side b = 10

• 0

• 1

• 2

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many solutions does the following SSA ambiguous case have? (BE CAREFUL - Look at the variables!) Given: angle C = 108.7^o, side a = 51.2, side c = 54.3

• 0

• 1

• 2

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11