Question

Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work

Answer 1

18.56 feet
Catie creates a similar triangle with the ladder so we can create a proportion to solve for the height.  
$\frac{baseto feet}{base to wall} = \frac{catie height}{wall height}$
Convert all values to feet . 16in = 1.33 ft . 5ft 6 in = 5.5 ft 
Insert values into proportions
$\frac{1.33}{4.5} = \frac{5.5}{x}$
Cross multiply to get
24.75=1.33x
divide both sides by 1.33
x=18.56ft