8 Calculate using Ptolemys methods the length of a noon shad

8. Calculate, using Ptolemy’s methods, the length of a noon shadow of a pole of length 60 at the vernal equinox at a place of latitude 40.

Solution

As per Ptolemy\'s method : At noon on the equinox the Sun will be vertically ahead at the Equator so the Sun\'s rays will make an angle of 40 degree with the pole.

Let l is the length of the shadow

Using the trigonometric ratio:
l/60 = tan 40
l = 60 tan 40 = 50.346 mt