Question

Find the perimeter of the figure

Answer 1

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

$tan(33^o)=\frac{8}{AD}$ ----> by TOA (opposite side divided by the adjacent side)

$AD=\frac{8}{tan(33^o)}=12.3\ units$

Find the length side BD

$sin(33^o)=\frac{8}{BD}$ ---> by SOH (opposite side divided by the hypotenuse)

$BD=\frac{8}{sin(33^o)}=14.7\ units$

step 2

In the right triangle CDE

Find the length side CE

$cos(64^o)=\frac{CD}{CE}$ --> by CAH (adjacent side divided by the hypotenuse)

we have

$CD=BD/2=14.7/2=7.35\ units$

substitute

$CE=\frac{7.35}{cos(64^o)}=16.8\ units$

Find the length side DE

$tan(64^o)=\frac{DE}{CD}$ --> by TOA (opposite side divided by the adjacent side)

$DE=tan(64^o){7.35}=15.1\ units$

step 3

Find the perimeter of the figure

The perimeter is equal to

$P=AB+AD+BD+CE+DE$

substitute the values

$P=8+12.3+14.7+16.8+15.1=66.9\ units$