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Geometry of using a ladder?
Posted on 2012-12-20
It's been a long time since I used geometry.
Extension ladder:
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.
http://nationalsafety.wordpress.com/2010/04/20/the-basics-of-extension-ladder-safety/
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?
--------------------------
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?
Extension ladder:
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.
http://nationalsafety.wordpress.com/2010/04/20/the-basics-of-extension-ladder-safety/
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?
--------------------------
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?
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12 Comments
Active today
The angle of the ladder is the arctangent of 4/1 = 75.9 degrees.
>> an extension ladder must extend 3 feet above the top landing.
This is if you have to step off the top of the ladder on to a roof or landing.
The top of any ladder at 75.9 degrees is
length x sin( 75.9) or length * 0.97
>> an extension ladder must extend 3 feet above the top landing.
This is if you have to step off the top of the ladder on to a roof or landing.
The top of any ladder at 75.9 degrees is
length x sin( 75.9) or length * 0.97
If 3 feet over the top and 3 feet overlap of the two sections, we're down to 22 feet before the angle.
Active today
The angle at the building is 14 degrees at the ground 76 degrees.
Arctangent (1/4) = 14 degrees (top angle). The ground angle is (90-14) degrees = 76 degrees. Accurate to within about 0.04 degrees plus or minus.
|\
| \ the hypotnuse is sqrt of 17
| \ 4 vertical units
|____\ ground angle
1 horizontal unit
Arctangent (1/4) = 14 degrees (top angle). The ground angle is (90-14) degrees = 76 degrees. Accurate to within about 0.04 degrees plus or minus.
|\
| \ the hypotnuse is sqrt of 17
| \ 4 vertical units
|____\ ground angle
1 horizontal unit
Active today
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.
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.
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.
Active today
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.
Active 1 day ago
You don't really need to know the angle to determine the maximum height a 28 ft. ladder can reach. Knowing you need a 3 ft. extension means the hypoteneuse will be 25 ft. so
25^2 = x^2 + (x/4)^2 = x^2 + x^2/16 ==> multiplying both sides by 16
16*25^2 = 17*x^2
16*625 = 17*x^2
10000 = 17*x^2 ==> dividing both sides by 17
10000/17 = x^2
588.24 = x^2 ==> taking the square root of both sides
24.25 = x ==> the maximum height the ladder will reach
6.125 ==> is the distance the base of the ladder will be from the wall
25^2 = x^2 + (x/4)^2 = x^2 + x^2/16 ==> multiplying both sides by 16
16*25^2 = 17*x^2
16*625 = 17*x^2
10000 = 17*x^2 ==> dividing both sides by 17
10000/17 = x^2
588.24 = x^2 ==> taking the square root of both sides
24.25 = x ==> the maximum height the ladder will reach
6.125 ==> is the distance the base of the ladder will be from the wall
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