There is a ladder 34ft long leaned against a wall. The bottom of the ladder is 30 feet away from the bottom of the wall. How tall is the wall?

Question

the second part is: If someone were to kick the ladder and it would move 4 more feet away from the wall how tall is the bottom of the wall to the top of the ladder? if someone were standing at the end of the ladder looking up at the top of it, what would be the angle of elevation? (at this point it would be 34 feet away from the wall but the length of the ladder stays the same as at the beginning) This is in a trigonometry/geometry unit so you’ll probably need to use pythagorean theorem and things like tan, sin, and cos. Thanks!

Answer 1

Pythagorean says:

34^2 = 30^2 + h^2 where H is the distance from the top of the ladder to the floor

1156 = 900 h^2

256 = h^2

h = 16

the distance from the top of the ladder to the floor is 16 ft.

the wall is taller.

Next, the base of the ladder is kicked 4 feet further away from the wall, making it 34 feet away.

However the ladder is exactly 34 feet as given. so it hits the ground. notice in the pythagorean

equation above, the height shall be zero.

So we put the ladder back to where it was... 30 feet away. That was right triangle ABC with dimensions AC=30 , BC=16, AB=34

Finally

tan BAC = BC/AC = 16/30 = 8/15

the angle is inverse tangent of 8/15 which is just over 28 degrees