You see two balls in the distance.The blue ball is half a degree across and rests half of a football field away.The red ball is one-quarter of a degree across and rests two football fields away.The red ball is ________ as large as the blue ball.
A) one-quarter
B) one-half
C) two times
D) four times

Question

Quizplus · Accepted Answer

The size of the ball is inversely proportional to the angle it subtends at the observer's eye.

Let's first calculate the actual size of each ball using simple trigonometry:

For the blue ball: 
tan(0.5 degrees) = opposite/hypotenuse 
tan(0.5 degrees) = x/(0.5*100)  [since the ball is half a degree across and half a football field away] 
x = 0.00436 miles or 23 feet (approx)

For the red ball: 
tan(0.25 degrees) = opposite/hypotenuse 
tan(0.25 degrees) = x/(2*100)  [since the ball is one-quarter of a degree across and two football fields away] 
x = 0.00436 miles or 46 feet (approx)

So, the red ball is about twice the size of the blue ball: 
46/23 = 2

Therefore, the answer is C) two times.

You See Two Balls in the Distance