Question

A device used in golf to estimate the distance d, in yards, to a hole measures the size s, in inches, that the 7-ft pin appears to be in a viewfinder. The viewfinder is held 9 inches from the viewer's eye. Express the distance d as a function of s

Answer 1

This is a proportional problem.
The distance 'd' corresponds to the 9 inches.
The 7-ft pin corresponds to the size 's'.

Convert 7ft to 7/3 yds. This way you have equal ratio of yds to inches.

$\frac{d}{9} = \frac{7/3}{s} \\ \\ d = \frac{21}{s}$

Answer 2

Answer:

d = $\frac{21}{s}$ yards

Step-by-step explanation:

This problem can be easily solved using proportionality/ratio between similar geometric figures.

Drawing a triangle from the viewers eye to the pin, up the pin, and back to the viewer's eye; and drawing a 2nd triangle from the viewers eye to the edge of the viewfinder up to the apparent height of the pin (the image) in the viewfinder and back to the viewer's eye gives two similar triangles.

The ratio of the height of the image in the viewfinder to the horizontal length between the viewer's eye and the viewfinder (9in) is equal to the ratio of the pin height (8/3 yards) to the distance d from the viewer to the pin, in yards.

The 7 ft pin is 7/3 yards tall. We need to express the pin height in yards so the units will cancel when we take the ratio with distance 'd'.

finding these ratios we can write:

$\frac{s}{9}$ = $\frac{7/3}{d}$

d x s = $\frac{7}{3}$ x 9

d = $\frac{21}{s}$ yards