Circumference and Trigonometry?

📌 CONCEPT: This problem involves using trigonometry to find the length of the shadow of a light source at the top of a Ferris wheel, given the central angle and the distance between the light source and the bottom of the wheel.

📐 RULE / FORMULA: To solve this problem, we can use the tangent function, which is defined as tan(θ) = opposite side / adjacent side. In this case, θ = 90°, and the opposite side is the height of the Ferris wheel, while the adjacent side is the distance from the light source to the bottom of the wheel.

💡 WORKED EXAMPLE: Given that the radius of the Ferris wheel is 20 meters, we can find the length of the shadow of the light source at the top of the wheel using the formula tan(90°) = height / (30 + x), where x is the length of the shadow. We can rearrange this formula to find x: x = (30 * 20) / 20 = 30 meters.

⚠️ COMMON MISTAKE: Students may get the wrong answer by forgetting to consider the central angle and using the wrong trigonometric function, or by not setting up the correct equation.