A handy man knows from experience that his 29-foot ladder rests in its most stable position when the distance of its base from a wall is 1 foot farther than the height it reaches up the wall. 1) how far up a wall does this ladder reach? 2) how far should the base be from the wall? 3) If the man needs to reach a window 25feet high on the wall, how far from the wall should he place the base of the ladder?

Question

A handy man knows from experience that his 29-foot ladder rests in its most stable position when the distance of its base from a wall is 1 foot farther than the height it reaches up the wall. 1) how far up a wall does this ladder reach? 2) how far should the base be from the wall?  3) If the man needs to reach a window 25feet high on the wall, how far from the wall should he place the base of the ladder?

phi · Answer

Did you draw a figure, and label what you know ?

phi · Answer

can you draw a figure ?

phi · Answer

How about this
 29-foot ladder
|dw:1443126395170:dw|

anonymous · Answer

I know how to make the drawing the problem is i do not know how to solve the problem

phi · Answer

Using this info:
the distance of its base from a wall is 1 foot farther than the height it reaches up the wall. 

and if we call the (unknown) height x, what is the distance along the ground ? (i.e. the bottom of the triangle) ?

anonymous · Answer

x+1

anonymous · Answer

i need help with part 2 and 3 of the question im not sure how to solve the problem and come up with the answer

phi · Answer

yes, that is good.
|dw:1443126847208:dw|

phi · Answer

You have a right triangle.  Do you know pythagoras formula?

anonymous · Answer

yes

phi · Answer

can you write down the formula, but using the sizes in the drawing ?  i.e. legs are x and (x+1) and the hypotenuse is 29

anonymous · Answer

I HAVE ALREADY COMPLETED that. I need help with part 2 and 3 of the question.

phi · Answer

what did you get ?

anonymous · Answer

the height of the wall is 20ft

phi · Answer

yes, so that means in the picture x=20
the base of the triangle is x+1
so you can figure   out answer to 2)

phi · Answer

For
 3) If the man needs to reach a window 25feet high on the wall, how far from the wall should he place the base of the ladder?

label a new figure
|dw:1443127849854:dw|

phi · Answer

I would write down pythagoras using those values
$$ x^2 +25^2 = 29^2 $$
can you solve for x ?

anonymous · Answer

is x 14?

phi · Answer

it's not exact. you need a calculator.  or type into google
sqrt(29^2 -25^2)=

you get 14.6969...

Do they ask you to round the answer ?

anonymous · Answer

yes thank you

phi · Answer

it rounds to 15 if you round to the nearest foot.