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The lengths of a shadow cast by a vertical gnomon (a device used to tell time) of heighth when the angle of the sun above the horizon is can be modeled by the equation h sin(90° - 8) 0° < 0 ≤ 90°. sin(8) (a) Verify that the expression for s is equal to h cot(e). S = S = = h sin(90° - 0) sin(8) sin(0) = h cot(0) (b) Use a graphing utility to complete the table of the lengths s for different values of 0. Let h = 5 feet. (Round your answers to two decimal places.) 0 S 15⁰ 30° 45° 60° 75° 90° 11.20 (c) Use your table from part (b) to determine the angle of the sun that results in the minimum length of the shadow.

The lengths of a shadow cast by a vertical gnomon (a device used to tell time) of heighth when the angle of the sun above the horizon is can be modeled by the equation h sin(90° - 8) 0° < 0 ≤ 90°. sin(8) (a) Verify that the expression for s is equal to h cot(e). S = S = = h sin(90° - 0) sin(8) sin(0) = h cot(0) (b) Use a graphing utility to complete the table of the lengths s for different values of 0. Let h = 5 feet. (Round your answers to two decimal places.) 0 S 15⁰ 30° 45° 60° 75° 90° 11.20 (c) Use your table from part (b) to determine the angle of the sun that results in the minimum length of the shadow.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 72E
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The lengths 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 can be modeled by the equation h sin(90° - 8) sin(8) 0° 0 ≤ 90°. (a) Verify that the expression for s is equal to h cot(Ⓒ). h sin(90° - 8) sin(8) S = S = = h cot(0) sin(0) (b) Use a graphing utility to complete the table of the lengths s for different values of 0. Let h = 5 feet. (Round your answers to two decimal places.) A S 15⁰° 30° 45° 60° 75° 90° 11.20 (c) Use your table from part (b) to determine the angle of the sun that results in the minimum length of the shadow.
Transcribed Image Text:The lengths 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 can be modeled by the equation h sin(90° - 8) sin(8) 0° 0 ≤ 90°. (a) Verify that the expression for s is equal to h cot(Ⓒ). h sin(90° - 8) sin(8) S = S = = h cot(0) sin(0) (b) Use a graphing utility to complete the table of the lengths s for different values of 0. Let h = 5 feet. (Round your answers to two decimal places.) A S 15⁰° 30° 45° 60° 75° 90° 11.20 (c) Use your table from part (b) to determine the angle of the sun that results in the minimum length of the shadow.
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