Chapter 4.2, Problem 63E

Solution

To identify: The total area of this rectangular collector panel locations between 20° and 60° north latitude, a solar collector panel should be mounted so that its angle with the horizontal is 20° greater than the local latitude. Consequently, the solar panel mounted on the roof of Solar Energy, Inc., in Atlanta (latitude 34°) forms a 54° angle with the horizontal. The bottom edge of the 12-ft-long panel is resting on the roof, and the high edge is 5 ft above the roof.

  

The total area of this rectangular collector panel is $\text{74}\text{.164}{\text{feet}}^{\text{2}}$

Given information

The given term is length of the rectangular collector panel is 12 feet long for breadth AC

Explanation:

Consider the given information

A=12h

Area of a rectangular is length times width. Let h be the hypotenuse of the triangle, and thus the unknown dimension of the rectangular solar panel.

  $\begin{array}{c}\sin 54°=\frac{5}{h}\\ h=\frac{5}{\sin 54°}\end{array}$

Therefore $A=12\cdot \frac{5}{\sin 54°}$

The relationship between the height h and the angle can be represent via the sine function solve for h and substitute into the first equation evaluating with a calculator to obtain result Take note that result will be in ${\text{feet}}^{\text{2}}$

So, $\text{74}\text{.164}{\text{feet}}^{\text{2}}$