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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 1 day ago
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 1 day ago
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 1 day ago
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 today
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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