Problem 921

Find the angular size of a circular object with a 3-inch diameter viewed from a  distance of 9 yards.




The formula for angular size is shown below.

Angular size =  physical size *\frac{360}{2\pi*distance}

Note that the physical size of the object (its diameter) is given inches, while the viewing distance is given in yards. Convert the viewing distance to inches.

1 yard = 36 inches

8 yards = 288 inches

Substitute into the formula.

Angular size = (3 in)*\frac{360}{2\pi*288 in}

Perform the calculations.

angular size = \frac{3*2*180}{2*\pi *3*288 in}

=\frac{180}{96\pi }

= \frac{15}{8\pi }


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