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16.. Which of the following scenarios would you be unable to use Law of Sines? *A. AASB. ASAC. SSAD. SSS

Question

16. Which of the following scenarios would you be unable to use Law of Sines?

  • A. AAS
  • B. ASA
  • C. SSA
  • D. SSS
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Solution

The Law of Sines can be used in the following scenarios:

A. Angle-Angle-Side (AAS): Yes, you can use the Law of Sines here. Once you have two angles, you automatically have the third because all the angles in a triangle add up to 180 degrees. Then, you can use the Law of Sines to find the missing sides.

B. Angle-Side-Angle (ASA): Yes, you can use the Law of Sines here. Once you have two angles, you automatically have the third because all the angles in a triangle add up to 180 degrees. Then, you can use the Law of Sines to find the missing sides.

C. Side-Side-Angle (SSA): Yes, you can use the Law of Sines here, but you have to be careful. This is the ambiguous case, where you could have one, two, or no triangles.

D. Side-Side-Side (SSS): No, you cannot use the Law of Sines here. You don't know any of the angles, so you can't set up a ratio. You would use the Law of Cosines in this case.

So, the scenario in which you would be unable to use the Law of Sines is D. Side-Side-Side (SSS).

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