The High Roller Ferris wheel in Las Vegas, the tallest in the world, is elevated 2 m above ground. When a car reaches the highest point on the ferris wheel, its altitude from ground level is 168 m. How far away from the center, horizontally, is the car when it is at an altitude of 120 m?
the radius of the wheel is ... (168 - 2) / 2 ... m
the altitude of the center is ... radius + 2 ... m
(horizontal distance)^2 + (distance above center)^2 = radius^2
To solve this problem, we need to use the concept of right triangle trigonometry, specifically the Pythagorean theorem. Here's how we can find the horizontal distance from the center of the High Roller Ferris wheel to the car when it is at an altitude of 120 m:
1. Let's assume that the center of the Ferris wheel is the origin of our coordinate system. Therefore, the car's highest point is at a height of 168 m from the ground (altitude) and is 2 m above the origin.
So, the coordinates of the highest point are (0, 168 + 2).
2. Now, let's consider the car's position when it is at an altitude of 120 m. We need to find the horizontal distance (x-coordinate) of this point.
3. From the information given, we know that the vertical distance (y-coordinate) of this point will be 120 m (as it is at an altitude of 120 m).
4. We have already determined the y-coordinate, so we need to find the x-coordinate. To do this, we can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the distance from the origin to the car) is equal to the sum of the squares of the other two sides of the right triangle formed.
Let's assume that the horizontal distance from the origin to the car is x (in meters).
Using the Pythagorean theorem:
x^2 + 120^2 = (168 + 2)^2
5. Now, we can solve the equation to find the value of x:
x^2 + 120^2 = 170^2
x^2 + 14400 = 28900
x^2 = 28900 - 14400
x^2 = 14500
x = √14500
x ≈ 120.41
Therefore, when the car is at an altitude of 120 m, it is approximately 120.41 meters away from the center horizontally.