Question

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)

Answer 1

`\displaystyle 10,7\:by\:the\:Law\:of\:Sines\:(SAS)`

Explanation:

First, find the angle measure of C:

`\displaystyle \\ \\ 180° = 65° + 21° + m∠C → 180° = 86° + m∠C \\ \\ 94° = m∠C`

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

`\displaystyle (c)/(sin∠C) = (b)/(sin∠B) = (a)/(sin∠A) \\ \\ (b)/(sin\:21°) = (27)/(sin\:65°) → 10,676212625... = (27sin\:21°)/(sin\:65°) \\ \\ 10,7 ≈ b`

I am joyous to assist you at any time.

Answer 2

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)