A ladder is resting against a wall. The ladder and the ground make an angle of 45° and the ladder is 7 ft from the wall. How long is the ladder?

The ladder, wall and floor form a right triangle, The angle where the wall and floor meets should be 90 degrees. We know the ladder and the ground makes an angle of 45 degrees, so the last angle must also be 45 degrees since all inner angles of a triangle add to 180.

In this case, we are looking for the hypotenuse. The question tells us the distance of one leg, 7 ft. Since the angle for the ladder and the wall is also 45 degrees, the second leg must also be 7 ft.

Plug this into the pythagorean theorem (a^2+b^2=c^2) where c is the hypotenuse.

49+49=c^2

98=c^2

c=approx 9.899

The final answer is about 9.899 ft