Designing a Ferris Wheel

📌 CONCEPT: To ensure that the riders experience a vertical displacement of 30 meters from the ground, Rahul needs to design the Ferris wheel at an angle of elevation that allows the riders to reach a height of 30 meters above the ground level.

📐 RULE / FORMULA: The sine function can be used to find the angle of elevation, where sin(angle) = opposite side (height) / hypotenuse (radius of the Ferris wheel).

💡 WORKED EXAMPLE: Given the radius of the Ferris wheel is 25 meters and the desired vertical displacement is 30 meters, we can use the sine function to find the angle of elevation. sin(angle) = 30 / 25 = 1.2. Using the inverse sine function, we can find the angle of elevation: angle = sin^(-1)(1.2) ≈ 50.2°.

⚠️ COMMON MISTAKE: Students often forget to consider the starting point of the wheel (ground level) and incorrectly assume the radius as the height, leading to an incorrect calculation of the angle of elevation.