Question

Determine the approximate value of x.

Answer 1

Answer:

  C.  6.736

Step-by-step explanation:

The unmarked angle is 180-80-40 = 60 degrees. Given the angles of the triangle and one side length there is enough information to use the Law of Sines to solve the triangle--eliminating choice D.

The angle opposite x is larger than the angle opposite 5, so x will be larger than 5. That leaves only answer choice C: 6.736.

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If you want to actually use the law of sines to determine x, you know that ...

  x / sin(60°) = 5 / sin(40°)

  x = 5·sin(60°)/sin(40°) . . . . . . multiply by sin(60°)

  x ≈ 6.736