A ladder 42 feet long is place so that it will reach a window 30 feet high (first building) on one side of a street; if it is turned over, its foot being held in position, it will reach a window 2o5 feet high (second building) on the other side of the street. How wide is the street from the building to building?
Your diagram is wrong. The ladder does not reach from one building to the other. Its foot is somewhere in the middle of the street, and it pivots so that it touches the first building at a height of 30', and the other at a height of 25'. Read the problem.
I assume that the second window is 25 feet high.
Draw a diagram. Let the foot of the ladder be x feet from the first building, and y feet from the second building. Using the good old Pythagorean Theorem, we have
x^2 + 30^2 = 42^2
y^2 + 25^2 = 42^2
so, x=29.39 and y=33.75, so the street is roughly 63 feet wide.
Thank you!! I trust you. :D
I hope this is right. :D
*This is my illustration
l
i\ l
i \ l
i \ l
i \ l
i____\l
-the 'l' is the 1st building.
-the 'i' is the 2nd building.
-the "backslash(\)" is the ladder.
-the "underscore(_)" is the street.
>is this right? :D
l
i\ l
i \ l
i \ l
i \ l
i____\l
woah! it doesn't look the way i made it. :( it's just look like letter 'N'. if it's fix.
A ladder 42 feet long is placed so that it will reach a window 30 feet
high on one side of a street. If it is turned over, its foot being held
in position, it will reach a window 25 feet high on the other side of
the street. How wide is the street from building to building?
To find the width of the street between the two buildings, we can use the Pythagorean theorem.
Let's assume that the distance from the first building to the point where the ladder touches the ground is x (in feet).
Using the Pythagorean theorem, we can set up the following equation for the first building:
x^2 + 30^2 = 42^2
Simplifying the equation, we have:
x^2 + 900 = 1764
x^2 = 864
Now let's assume that the distance from the second building to the point where the ladder touches the ground is y (in feet).
Using the Pythagorean theorem, we can set up the following equation for the second building:
y^2 + 205^2 = 42^2
Simplifying the equation, we have:
y^2 + 42025 = 1764
y^2 = 42025 - 1764
y^2 = 40261
Therefore, the width of the street is the sum of x and y, which is:
Width = x + y
Width = sqrt(864) + sqrt(40261)
Width ≈ 29.39 + 200.65
Width ≈ 230.04 feet
So, the width of the street between the two buildings is approximately 230.04 feet.