Greenwood press

SQUARE ROOTS
125
The Pythagorean theorem can be used
to determine the maximum viewing
distance, v, a pilot has in an airplane
compared with its altitude, a.
Note: this drawing is not to scale.

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from a painting is based on how much higher the bottom of the painting is from
a person’s eye level, 
b, and how much higher the top of the painting is from a per-
son’s eye level, 
t, according to the equation d =
√
bt.
If the average human is about 67 inches tall, and a large painting is 60 inches
tall, and the bottom is placed about 70 inches from the ground, then 
b =
70 − 67 = 3, and t = 3 + 60 = 63. Therefore a reasonable place to draw a view-
ing line would be about 14 inches away from the wall based on evaluating
d =
√
3 · 63 ≈ 13.7 inches. This formula can be applied to similar venues, such
as helping you find the best seat in a movie theater.
online sources for further exploration
Best angle of view

Bouncing ball

Calculating angles in a pyramid

Distance between two ships

How to compute baseball standings

Latitude and longitude

The square root law of inventory

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