Question

What is the length of EF?

Answer 1

Answer:

  (a)  3.8

Step-by-step explanation:

The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.

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compare angles

The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.

compare sides

Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.

  EF > DE

  EF > 3

Only one answer choice satisfies this inequality.

  EF = 3.8

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Additional comment

If you want to do the actual computation, we have ...

  EF/sin(D) = DE/sin(F)

  EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828

  EF ≈ 3.8