Two people enter a whispering gallery and want to know where they should stand so they can hear the other person's whisper. The gallery is 100 feet wide and the vertical distance from their head to the peak of the ceiling is 30 ft.

The two people should stand 40 feet from the center so that they can hear each other whisper

Step-by-step explanation:

From the question

Width of the gallery = 100 feet

Width = 2a

a = Width/2

a = 100/2 = 50 feet

Height of the gallery = b = 30 feet

Hence, the distance is

d² = a² - b²

d = √a² - b²

d = √50² - 30²

d = √2500 - 900

d = √1600

d = 40 feet

Hence, the two people should stand 40 feet from the center so that they can hear each other whisper.