Solar Panel Alignment?

📌 CONCEPT: To maximize sunlight on a solar panel, we need to find the angle at which the solar panel should be aligned with the sun's rays, considering the given angles of the panel with the horizontal and the sun's rays with the vertical.

📐 RULE / FORMULA: We can use the concept of complementary angles to find the required angle. The sum of the angles of the sun's rays with the vertical and the solar panel with the horizontal will give us the angle of the solar panel with the horizontal.

💡 WORKED EXAMPLE: Given that the sun's rays make an angle of 58° with the vertical and the solar panel is installed at an angle of 35° to the horizontal, we can find the required angle of the solar panel with the horizontal: Required angle = 90° - (58° + 35°) = 90° - 93° = -3°. However, a negative angle doesn't make sense in this context. We can find the correct angle by subtracting the sum of the given angles from 90°: Correct angle = 90° - (58° + 35°) = 90° - 93° is wrong. We must use 90° - (90° - 58°) - 35° instead. The correct angle is: 90° - (90° - 58°) - 35° = 58° - 35° = 23°.

⚠️ COMMON MISTAKE: Students often make a mistake of directly subtracting the sum of the given angles from 90°, which leads to an incorrect result.