Depth of a Well?

📌 CONCEPT: The depth of a well can be calculated using the angle of depression and the height of the well, involving the application of trigonometric functions.

📐 RULE / FORMULA: The tangent function can be used to find the distance of the well from the sea level, given by tan(θ) = opposite side (height of the well) / adjacent side (distance from the sea level).

💡 WORKED EXAMPLE: Given the angle of depression θ = 60° and the height of the well h = 10 meters, we can find the distance from the sea level x using the formula tan(60°) = 10 / x. Since tan(60°) = √3, we have √3 = 10 / x, which gives x = 10 / √3 = 5.77 meters (approximately).

⚠️ COMMON MISTAKE: Students often confuse the angle of depression with the angle of elevation and use the wrong trigonometric ratio, leading to incorrect calculations.