If a door measures 78in tall by 35in wide will an entertainment center measuring 60in x 48in x 48in fit through it? Im not even sure where to start!

Answer 1

Of course you know where to start. Draw a picture!

You're clearly going to have to tip the entertainment center. So, suppose the bottom corner is x from one side of the door, and y from the other side.

On the x side, the base of the e.c. reaches up to a height z. Since the height of the e.c. is 60", it will reach up (5/4 z) high. So, now you just have to solve

x+y=35
x^2+z^2 = 48^2
y^2+(5/4 z)^2 = 60^2

Do that and you will find that
(x,y,z) = (15.55,19.44,45.41)

The e.c. will fit exactly at that point. Chances are, there's a bit of wiggle room as well.

I must say, a 48" deep e.c. is some cabinet!

Answer 2

Well, that solution won't work, because the top corner of the tipped e.c. is higher than 73".

So, I think it will not fit.

Answer 3

What if it was 48in high?

Answer 4

Oh, yeah. I didn't think of tipping it on its side first. Well, try the same equations, but substituting in 48 for 60.

Good catch.

Answer 5

Ok. How about this.

If the e.c. is tipped up at an angle x, we need

48cos(x) + 48sin(x) <= 35
48√2 cos(π/4 - x) <= 73

Now, the e.c. just fits across when x = 10.4°

So, any angle higher than that will still fit, since the top corner will never be higher than 48√2 = 67.88" high