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Will Schultz

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3y ago
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8y ago

To solve this, we used the theorem of Pythagorus which states that in a right angle triangle:

a^2 + b^2 = c^2 (where ^2 means to the power roof 2 or squared)

In the case of this ladder, c=25 and a=7

==> b^2 = 25^2 - 7^2 = 625 - 49 = 576

==> b = sq rt (576) = 24.

In fact this is the week known 7, 24, 25 right triangle.

The ladder reaches 24 feet up the side of the building.

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Q: A painter placed a 25 foot ladder against a wall thw base of the ladder was 7 feet from the side of the building How high on the wall did the ladder reach?
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A 40 foot ladder is placed against a building the ladder forms a 75 degree angle with the ground How high up the building does the ladder reach?

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8 foot ladder how far from the wall should you place the base of the ladder?

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How long must a ladder be if it is placed 6 feet from a wall that is twenty four feet high?

That's going to depend heavily on two things:-- Do you want to be able to stand the ladder up and lean it against the wall ?-- How high above the ground do you want the ladder to hit the wall ?You haven't really said anything about these specifications in your question.If you want the ladder to lean against the wall, and hit it exactly at the top that is24-ft high, then the length of the ladder must besqrt( [6]2 + [24]2 ) = sqrt( 36 + 576 ) = sqrt(612) = 24.739 ft (rounded)


A 12-foot extension ladder is placed against a wall To achieve the proper climbing angle approximately how far should the bottom of the ladder be from the base of the wall?

I've heard it said that the vertical should be 4 times the size of the base (of the right angle triangle). Therefore if a 12 foot ladder would reach about an 11 foot vertical, it would be placed just under 3 feet from the wall.I've also seen it said that the angle should be 75.5 degrees.Personally I do not agree with an absolute. At heights under 10 feet, your center of gravity (especially if you are a very large person) might cause the ladder to move away from the wall while you are climbing, therefore a more shallow angle may be appropriate.At heights over 20 feet, I like to ensure good pressure against the wall when I am at the top. This feels more secure on a windy day. A more shallow angle can help, but ONLY if the base of the ladder is braced. For instance I've braced the bottom against a big tree, or a long plank that spans between the two wheels of a car.At heights over 25 feet especially you've just got to rule out all variables because it only takes one fall in a thousand trips up a ladder to end your fun (income, health, life). Stand back and look at your angles, test how the ladder feels as you go up, adjust as many times as you have to, brace the bottom, tie off the top, never compromise.


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