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Order the sides of the triangle from longest to shortest. E 99 42 39 D

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we can find the measurement of the sides of a triangle with its angles we need a formula


(ED)/(\sin\angle F)=(DF)/(\sin\angle E)=(FE)/(\sin\angle D)

we can take a couple and replace


\begin{gathered} (ED)/(\sin(42))=(DF)/(\sin(99)) \\ \\ (ED)/(\sin(42))=(DF)/(\sin(99)) \\ \\ (ED)/(0.67)=(DF)/(0.987) \\ ED=(DF(0.67))/(0.987) \\ ED=0.678DF \end{gathered}

take other couple


\begin{gathered} (DF)/(\sin(99))=(FE)/(\sin(39)) \\ (DF)/((0.987))=(FE)/(0.63) \\ DF=(FE(0.987))/((0.63)) \\ \\ DF=1.56FE \end{gathered}

other couple


\begin{gathered} (ED)/(\sin(42))=(FE)/(\sin(39)) \\ \\ (ED)/((0.67))=(FE)/((0.63)) \\ \\ ED=1.06FE \end{gathered}

we have 3 equations with 3 unknowns


\begin{gathered} 1.\text{ }ED=0.678DF \\ 2.\text{ }DF=1.56FE \\ 3.ED=1.06FE \end{gathered}

with this expression I can conclude some things


\begin{gathered} EDFE \\ ED>FE \end{gathered}

now, organize


DF>ED>FE

User Premshankar Tiwari
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