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In △DEF, what is the length of segment DF?

Right triangle DEF with DE measuring 27, angle F measures 60 degrees and angle E measure 90 degrees.

54
18 radical 3
27 radical 2
9

In DEF What Is The Length Of Segment DF Right Triangle DEF With DE Measuring 27 Angle F Measures 60 Degrees And Angle E Measure 90 Degrees 54 18 Radical 3 27 Ra class=

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Answer:

DF = 18√3

Step-by-step explanation:

Considering the angle 60⁰, opposite side = DE = 27, hypotenuse = DF = ?

Using Trigonometric ratio,

sin 60⁰ = 27 / DF

DF sin 60⁰ = 27

DF × √3 / 2 = 27 Divide both sides by √3 / 2

DF = 27 × 2 / √3

DF = 54 / √3 By Rationalizing

DF = 54 / √3 × √3 / √3

DF = 54√3 / 3

DF = 18√3

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