Question

question suppose we have a whispering chamber that is 12 feet wide and 26 feet long. if two people standing at the foci of this room can hear one another, approximately how far apart are they standing? select the correct answer below: 9 ft 15 ft 23 ft 27 ft

Explanation:

Step1: Identify the semi - major and semi - minor axes

The width of the whispering chamber is 12 feet, so the semi - minor axis $b = \frac{12}{2}=6$ feet. The length is 26 feet, so the semi - major axis $a=\frac{26}{2} = 13$ feet.

Step2: Use the formula for the foci of an ellipse

The relationship for the foci of an ellipse is $c=\sqrt{a^{2}-b^{2}}$. Substitute $a = 13$ and $b = 6$ into the formula: $c=\sqrt{13^{2}-6^{2}}=\sqrt{169 - 36}=\sqrt{133}\approx11.53$.

Step3: Calculate the distance between the foci

The distance between the foci is $2c$. So $2c\approx2\times11.53 = 23.06\approx23$ feet.

Answer:

23 ft