In △ABC, m∠A=19°, a=13, and b=14. Find c to the nearest tenth.

  c is either 25.4 or 1.1

Step-by-step explanation:

The Law of Sines is used to find sides and angles when you have a side and its opposite angle. Since the given angle is not opposite the longest given side, there are two possible solutions.

a) sin(B)/b = sin(A)/a

  sin(B) = (b/a)sin(A) = 14/13·sin(19°) ≈ 0.350612

  B = arcsin(0.350612)   or   180° -arcsin(0.350612)

  B = 20.525°   or   159.475°

Then angle C is ...

  C = 180° -A -B = 161° -B = 140.475°   or   1.525°

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Side c can be found from ...

  c = sin(C)·a/sin(A)

For C = 140.475°, ...

  c = sin(140.475°)·39.9302 ≈ 25.4

For C = 1.525°, ...

  c = sin(1.525°)·39.9302 ≈ 1.1

The length of side c could be 25.4 or 1.1.

898.1666667

step-by-step explanation:

5389/6 = 898.1666667