Finding the Angle of Elevation?

📌 CONCEPT: The angle of elevation is the angle formed by the line of sight to the top of an object and the horizontal line from the observer's eye to the base of the object. It is used to find the height or distance of the object from the observer.

📐 RULE / FORMULA: We can use the tangent function to find the distance of the pole from the building, given by the formula tan(θ) = opposite side (height of the building) / adjacent side (distance from the building). In this case, θ = 60° and the height of the building is 10 metres.

💡 WORKED EXAMPLE: Let's use the formula to find the distance of the pole from the building. Given θ = 60° and height of the building = 10 m, we can rearrange the formula to get distance = height / tan(θ) = 10 / tan(60°). Using a calculator, we find that tan(60°) ≈ 1.732, so the distance ≈ 10 / 1.732 ≈ 5.77 m.

⚠️ COMMON MISTAKE: Students often forget to use the correct value of θ in the formula or make a calculation error when finding the value of tan(θ).