Trigonometry in Flight

📌 CONCEPT: Trigonometric functions can be used to find the horizontal distance from the aircraft to a point on the ground directly below it by using the angle of elevation and the altitude of the aircraft.

📐 RULE / FORMULA: We can use the tangent function, tan(θ) = opposite/adjacent, where θ is the angle of elevation, to find the horizontal distance, which is the adjacent side. The formula is x = 5000/tan(θ), where x is the horizontal distance.

💡 WORKED EXAMPLE: Given the altitude of the aircraft is 5000 meters and the angle of elevation is 60°, find the horizontal distance. First, we need to find the value of tan(60°), which is √3. Then, we can use the formula x = 5000/√3 to find the horizontal distance, which is approximately 2886 meters.

⚠️ COMMON MISTAKE: Students may forget to use the correct trigonometric function or may not convert the angle from degrees to radians before using it in the formula, which can lead to incorrect results.