One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) is 7 5 8 feet by 5 3 8 feet. Astronauts on the Apollo missions had a flag on a shoulder patch, use the scale factor 1/60 and find the union dimensions for the patch

0.127 feet by 0.090 feet

Step-by-step explanation:

Given that :

The USA's flag dimension = 19feet by 10feet

Union's (blue rectangle in the top left corner) dimension = 7 5/8 feet by 5 3/8 feet.

Union dimension for the shoulder patch of the USA flag used by astronauts for the Apollo mission has a scale factor of 1/60

Therefore, dimension of the union patch ;

1/60 * ( 7 5/8 feet by 5 3/8 feet)

1/60 * (61 / 8 feet by 43/8 feet)

61/480 feet by 43/480 feet

0.127 feet by 0.0895 feet

0.127 feet by 0.090 feet

"Use Pythagorean Theorem to solve (a right triangle with the base being one of the side lengths and the height being the other side length.  a^2 + b^2 = c^2
64^2 + 100^2 = length of diagonal ^2
4096 + 10000 = 14096
The length of the diagonal is the square root of 14096 or 118.727 meters (rounded to the thousandths place). "
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