The length s of a shadow cast by a vertical gnomon (a device used to tell time) of

Chapter 6, Problem 79

(choose chapter or problem)

Why you should learn it (p. 497) The length s of a  shadow cast by a vertical gnomon (a device used to tell time) of height h when the angle of the sun above the horizon is \(\theta\) (see figure) can be modeled by

         \(s=\frac{h \sin \left(90^{\circ}-\theta\right)}{\sin \theta}\)

         

(a) Verify that the expression for s is equivalent to h \(\cot \theta\).

(b) Use a graphing utility to complete the table. Let h = 5 feet.

                   

(c) Use your table from part (b) to determine the angles of the sun that result in the maximum and minimum lengths of the shadow.

(d) Based on your results from part (c), what time of day do you think it is when the angle of the sun above the horizon is \(90^{\circ}\)?

Text Transcription:

theta

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

cot theta

90 degrees