## Newton’s Angle

Newton’s Angle
Sir Issac Newton was examining an angle formed by two segments joined on a piece of paper.  After using a protractor, he determined the measure (in degrees) of the angle to be one-fifth of the square root of forty-three less than the year he was born.  Sir Issac Newton uses his magnifying glass that magnifies everything three and one-half times the original size to view this angle.  What is the angle measure (in degrees) while viewing it under the magnifying glass?
Source: mathcontest.olemiss.edu 4/5/2010

SOLUTION
If you draw a right angle on a piece of paper and then look at it through a magnifying glass, it still looks like a right angle. Magnifying glass increases the size of objects but preserves the angles made by the objects.

Newtons’ birth year is 1643. Thus, the measure of the angle is
$\frac{1}{5}\left (\sqrt{1643-43}\right )=\frac{1}{5}\left (\sqrt{1600}\right )$
$=\frac{1}{5}\left (40\right )$
$= 8^\circ$
.

Answer: $8^\circ$.