Question

If a ladder 13m long leaning against a wall slides 1m down the wall, how long will be the new base if the previous base was 5m long?

If a ladder 13m long leaning against a wall slides 1m down the wall, how long will be the new base if the previous base was 5m long?

Answer 1

I think it would become about 6.92. You just need to use cos=x/r and sin=y/r relationships to determine the height. Then repeat with the height reduced by one.

Answer 2

wat?

Answer 3

okay so draw a triangle with the hypotenuse being 13 and the base being 5. You know that the cosine of the angle in that triangle could equal the base divided by the hypotenuse. Take the inverse cosine of that number of your calculator. Now you have an angle. You can now use the sine of that angle to equal the height divided by the hypotenuse, this gives you the height. Since it slides down one, reduce that number by one and use these same types of relationships to find the new base.

Answer 4

It's kind of a long way to solve it, but if you just go slow and use the relationships it actually isn't too bad.

Answer 5

Or apply the pythagorean theorem twice.
First, original height is:
\[\sqrt{13^2-5^2}=12\]
Then if it slides down one: New height is 11, now new base is:
\[\sqrt{13^2-11^2}=6.9282\]

Answer 6

There's the much easier way lol.

Answer 7

i need to solve this without any calculator

Answer 8

You can do 13 squared without one. And sqrt(144) =12
The tricky part will be the square root of 48 to get the final result.