Answer:
The perimeter is 66.9 units
Step-by-step explanation:
See the attached figure with letters to better understand the problem
step 1
In the right triangle ABD
Find the length side AD
[tex]tan(33^o)=\frac{8}{AD}[/tex] ----> by TOA (opposite side divided by the adjacent side)
[tex]AD=\frac{8}{tan(33^o)}=12.3\ units[/tex]
Find the length side BD
[tex]sin(33^o)=\frac{8}{BD}[/tex] ---> by SOH (opposite side divided by the hypotenuse)
[tex]BD=\frac{8}{sin(33^o)}=14.7\ units[/tex]
step 2
In the right triangle CDE
Find the length side CE
[tex]cos(64^o)=\frac{CD}{CE}[/tex] --> by CAH (adjacent side divided by the hypotenuse)
we have
[tex]CD=BD/2=14.7/2=7.35\ units[/tex]
substitute
[tex]CE=\frac{7.35}{cos(64^o)}=16.8\ units[/tex]
Find the length side DE
[tex]tan(64^o)=\frac{DE}{CD}[/tex] --> by TOA (opposite side divided by the adjacent side)
[tex]DE=tan(64^o){7.35}=15.1\ units[/tex]
step 3
Find the perimeter of the figure
The perimeter is equal to
[tex]P=AB+AD+BD+CE+DE[/tex]
substitute the values
[tex]P=8+12.3+14.7+16.8+15.1=66.9\ units[/tex]
