Chapter 8.7, Problem 5E

To determine

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

Answer to Problem 5E

On a longest day, the angle of elevation of the sun in the noon is $48\frac{1}{2}°$ .

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

Explanation of Solution

Given:

Approximate north latitude of Nome, Alaska is $64\frac{1}{2}°$ .

Calculation:

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

  $\begin{array}{l}=90°-\theta +23\frac{1}{2}°\\ =90°-64\frac{1}{2}°+23\frac{1}{2}°\text{ [Since }\theta =64\frac{1}{2}°]\\ =48\frac{1}{2}°\text{.}\end{array}$

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

  $\begin{array}{l}=90°-\theta -23\frac{1}{2}°\\ =90°-64\frac{1}{2}°-23\frac{1}{2}°\text{ [Since }\theta =64\frac{1}{2}°]\\ =2\frac{1}{2}°\text{.}\end{array}$