On Sun, 05 Jul 1998, Greg Milsom <[EMAIL PROTECTED]> wrote:
>... the sun's altitude in degrees for various times are as follows:
>4:00 -8.5
>5:00 1.6
>6:00 11.9
>7:00 23.1
>8:00 34.6
...
>The book states that all I must do is take the cotangent of these
>altitude numbers and multiply by the height of my perpendicular style
>(which is 2 inches) then measure out to the appropriate hour line. My
>problem is that I cannot figure out what a cotangent is or how to
>calculate one.
Hi Greg,
The cotangent is equal to the reciprocal of the tangent. Its use dates from
the
time before hand calculators when it was easier to multiply than to divide. So,
while Waugh is correct that you can multiply the style height by the cotangent
of the altitude, you will get the same answer if you *divide* the style height
by the *tangent* of the altitude.
Example: Your altitude for 8:00 a.m. is 34.6 degrees. The tangent of this
angle (from a calculator) is 0.68985. So the horizontal distance to the end of
the style's shadow is
2 / tan(34.6) = 2 / 0.68985 = 2.899 inches
-- Roger
*--------------------*
| Roger W. Sinnott |
| Associate Editor |
| Sky & Telescope |
*--------------------*
