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

We have been given that Catie's 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.

Upon looking at our attachment, we can see that Catie and Wall forms two right triangles with ladder sharing a common vertex.

To solve for h, we will use proportions as corresponding sides of similar triangles are proportional.

Let us convert our given measurements into inches.

1 feet = 12 inches.

4.5 feet = 12*4.5 inches = 54 inches

5 feet 6 inches = (5*12)+6 inches = 66 inches.

Using proportions, we can set an equation as:

[tex]\frac{h}{54}=\frac{66}{16}[/tex]

[tex]\frac{h}{54}*54=\frac{66}{16}*54[/tex]

[tex]h=4.125*54[/tex]

[tex]h=222.75[/tex]

Now, we will convert our answer into feet by dividing our answer by 12.

[tex]\frac{222.75}{12}=18.5625\approx 18.6[/tex]

Therefore, the ladder reaches 18.6 feet up-to the wall.

jainveenamrata jainveenamrata · Answer 2 · 2022-03-10T13:48:30+01:00

The ratio of the similar triangle remains constant. Then the ladder reaches 18.6 feet up to the wall.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

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 (5.5) tall.

Let h represent the height that ladder reaches up the wall.

Convert our given measurements into feet.

16 inches = 1.33

using proportion, we can set an equation as;

[tex]\rm \dfrac{h}{4.5} = \dfrac{5.5}{1.33}\\\\h \ \ = \dfrac{4.5*5.5}{1.33}\\\\h \ \ = 18.6[/tex]

Thus, the ladder reaches 18.6 feet upto the wall.

More about the triangle link is given below.

https://brainly.com/question/25813512