Question

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

Answer 1

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

$\frac{ED}{\sin\angle F}=\frac{DF}{\sin\angle E}=\frac{FE}{\sin\angle D}$

we can take a couple and replace

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

take other couple

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

other couple

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

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

$DF>ED>FE$