Question

Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.

Answer 1

Answers:

Answer to Problem 13 is 34.5

Answer to Problem 15 is 22.9

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Work Shown for Problem 13

sin(x)/17 = sin(91)/30

sin(x) = 17*sin(91)/30

sin(x) = 0.56658036

x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)

x = 34.51210645 or x = 180-34.51210645

x = 34.51210645 or x = 145.48789355

x = 34.5 or x = 145.5

If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).

If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)

In short, x = 34.5 is valid while x = 145.5 is not valid.

Therefore, the only possible answer is 34.5

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Work Shown for Problem 15

sin(x)/20 = sin(119)/45

sin(x) = 20*sin(119)/45

sin(x) = 0.38871987

x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)

x = 22.87486940 or x = 180-22.87486940

x = 22.87486940 or x = 157.1251306

x = 22.9 or x = 157.1

If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.

If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1

The only possible answer is therefore 22.9

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Side notes:

• Make sure your calculator is in degree mode. Unfortunately some calculators like to default to radian mode. A quick check is to see if sin(30) produces the result 0.5
• Arcsine is the same as inverse sine, which is denoted as
  `\sin^(-1)` on many calculators.