DEF is shown in the attachment.
Answer: x = 36.08
Step-by-step explanation: We can use Law of Sines to determine x, which is written as:
[tex]\frac{x}{sin(F)}=\frac{55}{sin(90)}[/tex]
where
F is the angle at vertex F
The angle is calculated knowing that the sum of all internal angles of a triangle is 180°:
F + 49 + 90 = 180
F + 139 = 180
F = 180 - 139
F = 41
Then, Law of Sines will be:
[tex]\frac{x}{sin(41)}=\frac{55}{sin(90)}[/tex]
Sin(90) = 1
sin (41) = 0.6560
Substituing and rearraging:
[tex]x=\frac{55}{1}(0.6560)[/tex]
x = 36.08
The value of x is 36.08 units
