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For each triangle shown below, determine whether you would use the Law of Sines or Law of Cosines to find angle x. Then find angle x to the nearest tenth.




68.3 by The Law of Cosines (SSS)

22.9 by The Law of Cosines (SAS)

10.7 by The Law of Sines (SAS)

8.8 by The Law of Sines (SSA)

For each triangle shown below determine whether you would use the Law of Sines or Law of Cosines to find angle x Then find angle x to the nearest tenth 683 by T class=

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carlosego
For this case using the law of the sine we have the following mathematical relationship:
 x / sine (21) = 27 / sine (65)
 Clearing x we have:
 x = (27 / sine (65)) * (sine (21))
 x = 10.68 units
 Rounding off we have:
 x = 10.7 units
 Answer:
 10.7 by The Law of Sines (SAS)
BasketballEinstein

Answer:

[tex]\displaystyle 10,7\:by\:the\:Law\:of\:Sines\:(SAS)[/tex]

Step-by-step explanation:

First, find the angle measure of C:

[tex]\displaystyle \\ \\ 180° = 65° + 21° + m∠C → 180° = 86° + m∠C \\ \\ 94° = m∠C[/tex]

Now that we have all three angles, we can proceed with the Law of Sines to solve for edge b:

[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{b}{sin\:21°} = \frac{27}{sin\:65°} → 10,676212625... = \frac{27sin\:21°}{sin\:65°} \\ \\ 10,7 ≈ b[/tex]

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