The lengths of a shadow cast by a vertical gnomonic a drives

The length\'s of a shadow cast by a vertical gnomonic (a drives used to tell time) of height h when the angle of the horizon is theta can be modeled by (A) Variety that the expression for s is equivalent to h cot(theta). (b) Use a graphing utility to complete the table. Let h = 5 feet.

Solution

s = h(sin(90 - theta)/sintheta

= hcos(theta)/sintheta

= hcot(theta)

h = 5ft

s = 5cot(theta)

theta = 15 ; s = 18.66

theta = 30 deg ; s = 8.66

theta = 45 deg ; s = 5

theta = 75 deg ; s = 1.339

theta = 90 deg ; s = 0

maximum shadow ; s = 18.66 ; theta = 18.66 deg

minimum shadow ; s = 0 ; theta = 0