Question

cuiuu allu ne internal factor method. 16. A new store is being planned near a neighborhood. The store will have a round sign, 10 feet in diameter, and will be up on a tall pole to make it widely visible. The sign will be 1000 feet away from some of the residents in the neighborhood (line of sight distance). Since the sign will be illuminated at night, the residents want to know which will appear bigger: the sign or the moon? The residents know you are an excellent math teacher, so they would like you to answer their question and explain the solution so that they can learn about the math that's involved. Please help out the residents! The moon is 384,000 km away and its diameter is 3,500 km. Di latiu)

Answer 1

Let P be the center of the round sign and Q be the center of the the moon. Now the radii of the round sign and the moon will be 10 / 2 feet and 3500 / 2 Km respectively. If the line joining the centers and the line of sight meets at point O (as shown in the figure below), then the two objects will appear of the same size if

$\dpi{100} {\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} d=\frac{10\times 2\; \; ft}{2\times 3500\; \; Km}\times 384000\; \; Km}$

or 3500 Km 2 10 384,000 Km

$\dpi{100} {\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; =\frac{38400}{35}\; \; ft}$

$\dpi{100} {\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; \cong 1097\; \; ft}$

The round sign will appear bigger if its distance from point O is less than d. Since 1000 < d, so the round sign will appear bigger than the moon.