Question

a painter leans a 15 foot ladder against a house the base of the ladder is 5 feet from the house how high on the house does the ladder reach

Answer 1

The ladder reaches approximately 14.14 feet high on the house.

Step-by-step explanation:

To determine how high on the house the ladder reaches, we can use the concept of similar triangles. In this case, the ladder forms a right triangle with the house. The length of the ladder is the hypotenuse, the base of the ladder is the adjacent side, and the height on the house is the opposite side.

Using the Pythagorean theorem, we can find the height on the house:

`Height on house = \sqrt{(ladder^2 - base^2)`

Plugging in the values from the question:

Height on house
`= \sqrt{(15^2 - 5^2)`

`= \sqrt{(225 - 25)`

`= \sqrt{200`

= 14.14 feet

Therefore, the ladder reaches approximately 14.14 feet high on the house.

Answer 2

`14.1\text{ ft}`

Step-by-step explanation:

Here, we want to get the height of the ladder from the ground

We start by drawing a diagrammatic representation of the information

We have this as follows:

Looking at the traingle, we can see a right triangle. This is indicated by the small box inside of the triangle

The side that faces the right angle is the length of the ladder which is 15 ft

It is the longest side and it is also referred to as the hypotenuse

We can use Pythagoras' theorem to find the missing length

According to the theorem,the square of the length of the hypotenuse equals the sum of the length of squares of the two other sides

mathematically,we have this as follows:

`\begin{gathered} 15^2=h^2+5^2 \\ 225=h^2\text{ + 25} \\ h^2\text{ = 225-25} \\ h^2\text{ = 200} \\ h\text{ = }\sqrt[]{200} \\ h\text{ = 14.1 ft} \end{gathered}`