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9514 1404 393

  (a)  6.2 cm

Step-by-step explanation:

You don't need to know much about trig here. You only need to know that the other acute angle in the triangle is less than 55°, so the measure of side x will be less than 8.9. Only one answer choice qualifies:

  x ≈ 6.2

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If you actually want to do the trig, as opposed to simply rejecting unreasonable choices, then you want to make use of the tangent relation.

  Tan = Opposite/Adjacent

  tan(55°) = 8.9/x

  x = (8.9 cm)/tan(55°) ≈ 6.23 cm

  x ≈ 6.2 cm