Answer:
13.8
Step-by-step explanation:
We can use trigonometry to find the length of DE
Remember these are the trigonometric ratios
Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
For ∠FDE we are given its opposite side length ( FE ) and need to find its adjacent angle ( DE )
When working with opposite and adjacent we use the trig ratio tangent
That being said we want to create an equation to solve for (DE) ( Recall that tan = opposite over adjacent. ) ( let DE = x )
so [tex]tan(51)=\frac{17}{x}[/tex]
now we solve for x
Step 1 multiply each side by x
tan(51) * x = x tan (51)
[tex]\frac{17}{x} *x=17[/tex]
now we have x tan (51) = 17
step 2 divide each side by tan (51)
[tex]\frac{xtan(51)}{tan(51)}=x\\\frac{17}{tan(51)}[/tex]
we now have
[tex]x =\frac{17}{tan(51)} \\[/tex]
[tex]tan(51)=1.234897157\\\frac{17}{1.234897157} =13.76632856[/tex]
we're left with x = 13.76632856
Finally we round to the nearest tenth and get that the answer 13.8
