# Geometry of using a ladder?

It's been a long time since I used geometry.

1. It is imperative that you understand that an extension ladder must extend 3 feet above the top landing.
3. The correct angle for an extension ladder should be ¼, meaning that for every 3-4 feet up, the ladder should be 1 foot out away from the base.
6. The sections of the extension ladder must overlap by at least 3 feet.

So, a 28 foot two piece extension ladder, would be about 7 feet from the base.
28 / 4 = 7.

A. What is the angle of the ladder in relation to perpendicular (straight up which would be 90 degrees)
B. If the two sections need to overlap 3 feet, and the top needs to be 3 feet above the landing, and the angle needs to be "x degrees from perpendicular," how high can this 28 foot ladder reach?

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I tried to draw a diagram using Paint but failed.

So, 7 feet from bottom of ladder to the building.
Top of ladder 3 feet above the top edge of building.
What is the angle and what is the height able to be reached?
d-glitch

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If both sections are 14 ft each, you really only have 25 ft ladder.

28 x .97 = 27.16 feet.

That does not allow for the two sections to overlap 3 feet.

If 3 feet over the top and 3 feet overlap of the two sections, we're down to 22 feet before the angle.
Yes, and the angle costs you 3%  or 7.9 inches.
SOLUTION

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The angles remain the same no matter the size of the triangle.  Maybe these are called congruent trangles I forget.  Use trig, easier for angles.
Note:  Oops, I didn't refresh before submitting.  My apologies to d-glitch.

If each unit is 1 foot, then your example is a 4 foot ladder (but using 16 for easy math = square root of 16 = 4)
The hypotenuse at 76 degrees would be 4 feet.
Since each unit is 1 foot then it's a 4 foot ladder, but it should lose 3% due to the angle.

Not sure if a 28 foot ladder would be 28 units. Yes, I think.
Being as I have worked as a safety engineer before, I must warn you to check the capacity tag on the side of any ladder you use.  Most are rated for 250 lbs which is not enough for me.  I have to buy construction rated ladders for big people carrying materials.
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