Question

So I'm currently doing online school due to external circumstances and haven't done this type of problem before. I need help finding DE and an explanation on how to get it, thanks!​

Answer 1

Answer:

  DE ≈ 14.91

Step-by-step explanation:

Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

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The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.

The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.

This means you have enough information to use these relations:

  tan(61°) = DF/CF = DF/24

  DF = 24·tan(61°)

and

  tan(19°) = DE/DF

  DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above

  DE ≈ 24(1.804048)(0.344328) ≈ 14.908

The length of DE is about 14.91.