1. How far is the Willis Tower from Navy Pier, given that each unit is approximately 1/8 mile? Round your answer to the nearest tenth of a mile.

Question

The Willis Tower is at the point (-6,-3) and NP is at the point (10,9).

I did this calculation: d^2 = (10 - (-6))^2 + (9 - (-3))^2 = d^2 = 256 + 144 = d = √400 = 20*1/8 = 2.5

Is this correct? also, I know it may be a dumb question, but what would the answer be when I round to the nearest tenth? Would it be 3?

2. Tom is buying a 42in plasma t.v.. The frame around the screen is 1 in wide. Will it fit his entertainment center that has an opening of 36 by 24 inches?

My work:

Okay, so because T.V.s are measured diagonally, we are trying to find the length of a hypotenuse.

24^2 + 36^2 = c^2
576 + 1296 = c^2
c = √1872 = 43.3

Now, because the frame is one inch, wouldn't that ad 1 inch to each corner? Therefore, the length of the hypotenuse in its entirety is 44 inches. Therefore the t,v. would NOT fit in the entertainment center that has an opening of 43.3 inches (diagonally).

Is this correct?

3. I have a box here (it's a rectangle box, not a cube). Its width is 12cm, the length is 9cm and the height is 8cm. I have to find the length of the diagonal line (the hypotenuse of an invisible triangle that goes through it.) Can you help me with this?

Thanks so much!

Answer 1

1 and 2 are correct, as far as I can figure out. You would leave number 1 as 2.5, if not a more complex decimal. As a mathmatician, you will always show the decimals to several points out. Scientists don't like this saying that extra decimals just create confusions. If you have ever heard of the relevant decimals theory, that is the basis. As for 3, try thinking of it as two separate triangles that share a side.