a. Explanation Given: The declination of sun i ° on summer solstice is i ° = 23.5 ° . The latitude of the location θ ° north latitude = 29 ° 45 ′ . Formula used: The approximate number of hours of daylight D when the declination of sun is i ° at a location θ ° north latitude for any date between the vernal equinox and autumnal equinox is given by the formula: D = 24 [ 1 − cos − 1 ( tan i tan θ ) π ] where cos − 1 ( tan i tan θ ) is expressed in radians. Calculation: Convert θ ° = 2 9 ° 4 5 ′ as follows: θ ° = 2 9 ° 4 5 ′ = 2 9 ° + 4 5 ′ 60 = 29.75 ° Apply the above formula to obtain the number of hours of daylight D in Houston, Texas on summer solstice as follows: First calculate cos − 1 ( tan i tan θ ) and express it in radians as follows: cos − 1 ( tan i tan θ ) = cos − 1 ( tan ( 23 b. To determine The approximate number of hours of daylight in Houston, Texas on vernal equinox. c. To determine The approximate number of hours of daylight in Houston, Texas on July 4.

Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)

11th Edition

ISBN: 9780136872689

Author: Michael Sullivan

Publisher: PEARSON+

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Question

Chapter 8.1, Problem 75AYU

To determine

The approximate number of hours of daylight in Houston, Texas on summer solstice.

To determine

The approximate number of hours of daylight in Houston, Texas on vernal equinox.

To determine

The approximate number of hours of daylight in Houston, Texas on July 4.

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Chapter 8.1, Problem 74AYU

Chapter 8.1, Problem 76AYU

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Chapter 8 Solutions

Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)

Ch. 8.1 - Prob. 1AYU Ch. 8.1 - Prob. 2AYU Ch. 8.1 - Prob. 3AYU Ch. 8.1 - Prob. 4AYU Ch. 8.1 - Prob. 5AYU Ch. 8.1 - Prob. 6AYU Ch. 8.1 - Prob. 7AYU Ch. 8.1 - Prob. 8AYU Ch. 8.1 - Prob. 9AYU Ch. 8.1 - Prob. 10AYU

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