Question

A ladder 15 feet long leans against a wall and forms an angle of 45º with the ground. How far from the wall is the ladder?

Answer 1

The ladder is the hypotenuse of a 45 45 90 triangle.
The legs of a 45 45 90 triangle = hypotenuse / sqroot (2)

15 / 1.414 = 10.608

(Incidentally it is the "bottom" of the ladder that is 10.608 feet from the wall. The "top" of the ladder is touching the wall. LOL)

Answer 2

The foot of the ladder is 10.60 feet from the wall.

Explanation:

A ladder 15 feet long leans against a wall and forms an angle of 45º with the ground.

The 15ft ladder forms a 45,45,90 degree right triangle with itself ; being the hypotenuse, the ground and the wall. This triangle has it's sides in the ratio of 1,1,√2

So, we know two sides will be same length and one side is 15 feet.

So, the ladder is
`(15√(2)) /2` feet from the wall .

Also the ladder goes same
`(15√(2)) /2` feet up the wall.

This becomes:

`(15*1.414)/2=10.60` feet

Hence, the measurements are 10.60 feet, 10.60 feet and 15 feet.

The foot of the ladder is 10.60 feet from the wall.