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A project was launched to establish the best fixed tilt angle at which solar panels should be installed to maximize annual energy output. The annual energy output is measured in kWh and represents the energy converted from sunlight to electrical energy available for use by electrical appliances.

Seven solar panels were installed in an open field, each at a different fixed tilt angle. The energy output of the seven panels was measured over a period of one year (365 days).

The results can be found in the table below:
\begin{tabular}{|c|c|c|}
\hline
Panel Number & \begin{tabular}{c}
Tilt (angle with the \\
horizontal plane)
\end{tabular} & \begin{tabular}{c}
Total Annual Energy Output of the Panel \\
(kWh/year)
\end{tabular} \\
\hline
1 & [tex]$0^{\circ}$[/tex] & 350 \\
\hline
2 & [tex]$10^{\circ}$[/tex] & 370 \\
\hline
3 & [tex]$20^{\circ}$[/tex] & 390 \\
\hline
4 & [tex]$30^{\circ}$[/tex] & 410 \\
\hline
5 & [tex]$40^{\circ}$[/tex] & 335 \\
\hline
6 & [tex]$50^{\circ}$[/tex] & 360 \\
\hline
7 & [tex]$90^{\circ}$[/tex] & 220 \\
\hline
\end{tabular}

4.1 Draw a bar graph to illustrate the annual energy output at different tilt angles for the seven solar panels.

4.1.1 Which tilt angle gives the highest annual energy output? (1)

Sagot :

GinnyAnsweridn
Let's break down the solution in two parts:

### Step 1: Draw the Bar Graph
To illustrate the annual energy output at different tilt angles for the seven solar panels, we draw a bar graph.

#### Data from the table:

- Panel Numbers: 1, 2, 3, 4, 5, 6, 7
- Tilt Angles (degrees): [tex]\(0^\circ, 10^\circ, 20^\circ, 30^\circ, 40^\circ, 50^\circ, 90^\circ\)[/tex]
- Annual Energy Output (kWh/year): 350, 370, 390, 410, 335, 360, 220

Let's layout the plot:

1. X-Axis: Represents the tilt angles of the solar panels.
2. Y-Axis: Represents the annual energy output in kWh/year.
3. Bars: The height of each bar will represent the energy output for each specified tilt angle.

Here's a description of how the bar graph should look:
- The bars will correspond to the tilt angles [tex]\(0^\circ, 10^\circ, 20^\circ, 30^\circ, 40^\circ, 50^\circ, 90^\circ\)[/tex].
- The height of each bar is aligned with the energy output values [tex]\(350\)[/tex], [tex]\(370\)[/tex], [tex]\(390\)[/tex], [tex]\(410\)[/tex], [tex]\(335\)[/tex], [tex]\(360\)[/tex], [tex]\(220\)[/tex] respectively.

### Step 2: Determine the Tilt Angle with the Highest Annual Energy Output

From the data:
- At [tex]\(0^\circ\)[/tex]: 350 kWh/year
- At [tex]\(10^\circ\)[/tex]: 370 kWh/year
- At [tex]\(20^\circ\)[/tex]: 390 kWh/year
- At [tex]\(30^\circ\)[/tex]: 410 kWh/year
- At [tex]\(40^\circ\)[/tex]: 335 kWh/year
- At [tex]\(50^\circ\)[/tex]: 360 kWh/year
- At [tex]\(90^\circ\)[/tex]: 220 kWh/year

To find the highest annual energy output, we compare the energy values and find the maximum.

#### Maximum Energy Output:
- The highest energy output is [tex]\(410\)[/tex] kWh/year.

#### Optimal Tilt Angle:
- The tilt angle corresponding to this energy output is [tex]\(30^\circ\)[/tex].

### Answer to the Question:

4.1.1 The tilt angle that gives the highest annual energy output is [tex]\(30^\circ\)[/tex].

By following these steps, you've plotted the bar graph and determined that a tilt angle of [tex]\(30^\circ\)[/tex] gives the highest annual energy output of [tex]\(410\)[/tex] kWh/year.
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