Solución a Problema de Viga y Corredores

[madin]

the problem is

Una viga tiene 25m de largo, y un corredor, cuya anchura es de 13m, comunica con otro corredor que se encuentra perpendicular al primero ¿Qué anchura mínima tiene que tener el segundo corredor para que pueda pasar la viga del primer corredor al segundo?

sorry i don't know how translate into english better
someone please help?

 

[madin]

You have a steel beam, 25m long.
A corridor, 13m wide.
A second corridor, perpendicular to the first.
How WIDE must the second corridor be to allow the steel beam to pass through?

Translate, this is very basic. thanks

 

[HallsofIvy]

Draw a picture. Draw the first corridor as two parallel lines, say vertical. Draw the second corridor as two horizontal parallel line meeting the first two. Now draw the "steel bar" (a single line) just] making it around the corner- that should extend from one outer wall, touch the corner where the inner walls meet to the outer wall.

You should see two right triangles. One of them has a side of length 13 m. If the angle the bar makes with the wall is θ so the length of the hypotenuse (length of the bar in that corridor is 13/sin(θ). Okay, the length of the hypotenuse of the other right triangle is the length of the steel bar minus that: 25- 13/sin(θ).
Since the angle the bar makes with the opposite wall is the complement of θ, if we call the width of the other corridor (which is what we are trying to find), x, then we have x/cos(θ)= 25- 13/sin(θ). Now the problem is to find the SMALLEST corridor that will allow the bar to go around the corner. Write x as a function of θ and find the value of θ that minimizes x and find the value of x corresponding to that.

 

[madin]

Is answer 5.25?

 

[HallsofIvy]

I get about 8.45 meters.


We can't tell what you did wrong if you don't show us what you did!

 

[madin]

i am so confused.. maybe i am readying what you wrote wrong, is there a way to do this without law of cosins and sins

sry for horrible english!

 

[madin]

is it okay to ask how you receive your answer?

 

[madin]

http://home.ripway.com/2004-6/130079/rox.JPG

 

[HallsofIvy]

Why assume a 45 degree angle?

 

[madin]

equation for minimum: x^{2/3} + 13^{2/3} = 25^{2/3}.
solving for x gives: x = (25^{2/3} - 13^{2/3})^{3/2} \approx 5.251080936.

what is the target function and not only the first order conditions, how to get there and, the most important thing What is the basic premise, to say, what is true problem? If someone could help me with this.. i'd really appreciate it. unles i am wrong

 

[madin]

May I have some comment please?

Is there a way to make this into one simple equation?