Chapter 8.7, Problem 9E

To determine

the desired value of overhang $x$ such that it shades the entire window at noon at the summer solstice.

Answer to Problem 9E

The angle of elevation at summer solstice is $39\frac{1}{2}°$ , and the value of $x=11\text{ ft}$ .

Explanation of Solution

Given:

The diagram shows the cross section of the wall that will face south ( $74°$ ).

Calcualtion:

Angle of elevation at summer solstice is,

  $\begin{array}{l}=90°-74°+23\frac{1}{2}°\\ =39\frac{1}{2}°.\end{array}$

Now, by the ratio of sides in a right − angled triangle, we can write:

  $\begin{array}{l}\sin 39\frac{1}{2}°=\frac{7}{x},\\ \Rightarrow x=\frac{7}{0.636},\\ \Rightarrow x=11\text{ ft}\text{.}\end{array}$