A dime is 1.8 cm in diameter. Earth's Moon is 3.844 × 10¹⁰ cm from Earth and has a diameter of 3.76 × 10⁸ cm. At what distance from your eye would you have to hold a dime so that it has the same angular diameter as the full Moon? A) 200 cm B) 2 cm C) 0.2 cm D) 2 AU E) 2 LY

Question

Quizplus · Accepted Answer

To have the same angular diameter, the ratio of the diameter to the distance must be the same for both the dime and the Moon. Using the formula for angular diameter, the distance from the eye to the dime is calculated as (1.8 cm / x) = (3.76 × 10^8 cm / 3.844 × 10^10 cm), solving for x gives approximately 200 cm.

A Dime Is 1