Question

a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.

Answer 1

`\huge\boxed{7.79 \ \text{feet}}`

Explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

|\

| \

x | \ 9

| \

| \

|_____\

4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that
`a^2+b^2=c^2`, where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

`a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79`

Hope this helped!