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!

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!

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.

What if it was 48in high?

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.

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

To determine if an entertainment center measuring 60 inches by 48 inches by 48 inches will fit through a door measuring 78 inches tall by 35 inches wide, you need to compare the dimensions of the entertainment center to the dimensions of the door.

First, focus on the height. The door measures 78 inches tall, so the height of the entertainment center, which is 60 inches, should fit through the door.

Next, consider the width. The door measures 35 inches wide, and the entertainment center is 48 inches wide. Since 48 inches is greater than 35 inches, the entertainment center might not fit through the door.

To determine for sure, you need to check the depth. If the depth of the entertainment center is less than the width of the door, it should fit.

In summary, the entertainment center's height is smaller than the door's height, indicating it will fit. However, the width may pose a problem unless the depth of the entertainment center is less than the width of the door. To be certain, you should also consider any additional factors, such as angles or obstructions near the door, that might affect the fit.