Chapter 8.7, Problem 1E

To determine

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

Answer to Problem 1E

On a longest day, the angle of elevation of the sun in the noon is $66°$ .

On a shortest day, the angle of elevation of the sun in the noon is $19°$ .

Explanation of Solution

Given:

Approximate north latitude of Seattle, Washington is $47\frac{1}{2}°$ .

Calculation:

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

  $\begin{array}{l}=90°-\theta +23\frac{1}{2}°\\ =90°-47\frac{1}{2}°+23\frac{1}{2}°\text{ [Since }\theta =47\frac{1}{2}°]\\ =66°\text{.}\end{array}$

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

  $\begin{array}{l}=90°-\theta -23\frac{1}{2}°\\ =90°-47\frac{1}{2}°-23\frac{1}{2}°\text{ [Since }\theta =47\frac{1}{2}°]\\ =19°\text{.}\end{array}$