Trigonometry mountain assessment problem

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In summary, the conversation discusses the task of calculating the lengths of horizontal and vertical timber supports for a roller coaster track in the shape of a sinusoid. The track has a horizontal separation of 50 meters and a vertical separation of 30 meters with the low point being 3 meters below ground. The problem asks for an equation expressing the vertical distance, y, in terms of the horizontal distance, x, using the standard form of a sinusoidal equation. The user has drawn a sketch of the graph and is seeking help in determining the values for a, b, c, and d in the equation.
  • #1
jenherting
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A portion of a roller coaster track is to built in the shape of a sinusoid. You have been hired to calculate the lengths of the horizontal and vertical timber supports to be used. The high and low points on the track are separated by 50 meters horizontally and by 30 meters vertically. The low point is 3 meters below ground. Let y be the number of meters the track is above the ground and x be the number of meters horizontally from the high point, write an equation expressing y in terms of x.
 
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  • #2
Hello and welcome to MHB, jenherting! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
  • #3
So far the work that I have was I drew a sketch of the graph itself and now I just need help on how to write the equation and what parts of the problem represents the aspects of a sinusoidal equation.
 
  • #4
jenherting said:
The low point is 3 meters below ground.

This seems odd. Are you sure it's not 3 meters above the ground?

You need an equation of the form

$$y=a\sin(bx+c)+d$$

Any thoughts on where to begin?
 

FAQ: Trigonometry mountain assessment problem

What is the "Trigonometry mountain assessment problem"?

The "Trigonometry mountain assessment problem" is a mathematical problem that involves using trigonometric functions to calculate the height of a mountain or elevation of a point on a mountain given the distance from a known point and the angle of elevation.

How is trigonometry used in the "Trigonometry mountain assessment problem"?

Trigonometry is used in the "Trigonometry mountain assessment problem" to calculate the unknown height or elevation using the known distance and angle of elevation. The trigonometric functions, such as sine, cosine, and tangent, are used to find the missing side lengths and angles in a right triangle.

What are the key steps to solving the "Trigonometry mountain assessment problem"?

The key steps to solving the "Trigonometry mountain assessment problem" are:
1. Identify the known and unknown values in the problem.
2. Draw a diagram and label the sides and angles of the triangle.
3. Use the appropriate trigonometric function (sine, cosine, or tangent) to set up an equation.
4. Solve the equation for the unknown value.
5. Check your answer by plugging it back into the original equation and making sure it satisfies the given information.

What are some real-world applications of the "Trigonometry mountain assessment problem"?

The "Trigonometry mountain assessment problem" has many real-world applications, such as:
- Determining the height of a building or structure from a distance.
- Calculating the slope or grade of a road or ramp.
- Finding the height of a tree or flagpole.
- Measuring the elevation of a point on a mountain or hill.
- Estimating the depth of a well or hole.

What are some tips for solving the "Trigonometry mountain assessment problem"?

Some tips for solving the "Trigonometry mountain assessment problem" are:
- Make sure to use the correct trigonometric function for the given information.
- Draw a clear and accurate diagram to visualize the problem.
- Label the sides and angles of the triangle correctly.
- Double-check your calculations for accuracy.
- If possible, use a calculator or trigonometric table to assist with calculations.
- Practice and review basic trigonometric concepts to improve your skills.

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