Finding the Angle: Solving Trig Problems on the Ferris Wheel

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In summary, the conversation discusses a problem about the Ferris Wheel and its height as a function of time. The given equation is used to represent the height of a seat on the wheel and the question asks for the time at which an individual is exactly 125 feet above the ground within the first 50 seconds of the ride. The conversation also suggests drawing a diagram to better understand the problem.
  • #1
urthatarget
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I have this question in my trig/pre cal class and I have no idea how to approach it what so ever.

In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then

h(t) = 125sin (pi/25t - pi/2) + 125

represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds. The ride begins when t = 0.


a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

Thank you!
 
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  • #2
Sometimes a diagram of the problem helps visualise the solution.
Draw the ferris wheel, add a line 125 feet off the ground, and find out what angle of rotation will bring the passenger to that height.
I have to stop now, and leave you with something to do!
 

1. What is the purpose of the "Ferris Wheel trig question"?

The "Ferris Wheel trig question" is a common math problem used to illustrate the application of trigonometry in real-life scenarios. It involves calculating the height of a person on a Ferris wheel at a given time using trigonometric functions.

2. How do you approach solving the "Ferris Wheel trig question"?

To solve the "Ferris Wheel trig question", you will need to draw a diagram and label the relevant angle measures and side lengths. Then, you can use trigonometric ratios (such as sine, cosine, and tangent) to set up and solve an equation to find the height of the person on the Ferris wheel.

3. Can you explain the concept of radians in relation to the "Ferris Wheel trig question"?

Radians are a unit of measurement for angles, commonly used in trigonometry. In the "Ferris Wheel trig question", the angle representing the position of the person on the Ferris wheel is measured in radians. This allows for more precise calculations and is necessary for solving the problem using trigonometric functions.

4. Are there any common mistakes to avoid when solving the "Ferris Wheel trig question"?

One common mistake when solving the "Ferris Wheel trig question" is confusing the angle measure given (in degrees) with the angle measure needed (in radians). It's important to convert between degrees and radians when necessary. Additionally, be careful with the signs of the trigonometric ratios, as they can change depending on the quadrant in which the angle is located.

5. What other real-life scenarios can be modeled using trigonometry?

Trigonometry is used in a variety of real-life scenarios, such as calculating the height of a building or tree, determining the distance between two objects, and finding the angle of elevation or depression. It is also used in fields such as engineering, navigation, and astronomy.

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