Finding Values

Create proportion

cross multiple $18=2\left(PR\right)$  

Solve for PR by dividing by 2

 $PR=9$  

Create proportion

cross multiply  $30=3\left(XY\right)$  

Divide by 3: XY = 10

create proportion

cross multiply  $24=2\left(QR\right)$  

Divide by 2: QR = 12

You could also use Pythagorean Theorem to solve for the missing sides

 $m\angle Z=90\degree$  means XZ and YZ are the legs

 $XY=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$  

In school we'd go outside with mirrors and estimate/measure trees, buildings, structures, etc

Yesterday's practice problems asked about this (it was #4)

All you need is your height, the distance you are from the mirror, and the distance the mirror is from your object

Then use similarity to solve the height of the building