Chapter 8.7, Problem 3E

To determine

the angle of elevation of the sun at noon on the longest day and shortest day.

Answer to Problem 3E

On a longest day, the angle of elevation of the sun in the noon is $83\frac{1}{2}°$ .

On a shortest day, the angle of elevation of the sun in the noon is $36\frac{1}{2}°$ .

Explanation of Solution

Given:

Approximate north latitude of Houston, Texas is $30°$ .

Calculation:

On a longest day, the angle of elevation of the sun in the noon is given by:

  $\begin{array}{l}=90°-\theta +23\frac{1}{2}°\\ =90°-30°+23\frac{1}{2}°\text{ [Since }\theta =30°]\\ =83\frac{1}{2}°\text{.}\end{array}$

And, on a shortest day, the angle of elevation of the sun in the noon is given by:

  $\begin{array}{l}=90°-\theta -23\frac{1}{2}°\\ =90°-30°-23\frac{1}{2}°\text{ [Since }\theta =30°]\\ =36\frac{1}{2}°\text{.}\end{array}$