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

`(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`