What is the solution to finding d(x) without using trigonometry?

In summary, the conversation discusses a homework problem that requires finding d(x) without using trigonometry or calculus. One person has already provided a solution involving trigonometry, but the other person suggests using similar triangle arguments and the Pythagorean theorem to solve it without trigonometry. The solution is then successfully found.
  • #1
1MileCrash
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Homework Statement



Attached

Homework Equations





The Attempt at a Solution



I am to provide a solution without using any trigonometry or calculus, but I can't find a way. To clarify, I must find d(x).

Involving trig, the problem is trivial, as the angle "A" is equal to arctan(5/4), and then the law of cosines is applied, this is my result on the attachment.

How could you solve this without involving trigonometry?
 

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  • #2
1MileCrash said:

Homework Statement



Attached

Homework Equations





The Attempt at a Solution



I am to provide a solution without using any trigonometry or calculus, but I can't find a way. To clarify, I must find d(x).

Involving trig, the problem is trivial, as the angle "A" is equal to arctan(5/4), and then the law of cosines is applied, this is my result on the attachment.

How could you solve this without involving trigonometry?

Drop a perpendicular from C to AB. I think you can use similar triangle arguments and the Pythagorean theorem to get a relationship between x and d without using the law of cosines.
 
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  • #3
Cheers, solution followed readily.
 

FAQ: What is the solution to finding d(x) without using trigonometry?

What is the definition of length as a function of x?

Length as a function of x refers to the measurement of distance or extent along the x-axis of a graph or coordinate system. It represents the relationship between the independent variable x and the dependent variable, which is the length in this case.

How is length as a function of x represented on a graph?

Length as a function of x is typically represented by a line or curve on a graph. The x-axis represents the input values or independent variable, while the y-axis represents the output values or dependent variable. The line or curve on the graph shows the relationship between the two variables.

What is the importance of understanding length as a function of x?

Understanding length as a function of x is essential in various fields of science, such as physics, engineering, and mathematics. It allows us to analyze and predict how the length of a system or object changes with respect to the input variable x. This knowledge is crucial in problem-solving and making accurate measurements and calculations.

How is the length as a function of x calculated?

The calculation of length as a function of x depends on the specific function or equation that represents the relationship between the two variables. For linear functions, the length can be calculated using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. For more complex functions, it may require using calculus or other mathematical techniques to find the length.

Can length as a function of x change over time?

Yes, length as a function of x can change over time, depending on the system or object being measured. For example, the length of a spring may change as it is stretched or compressed, which can be represented by a function of x. In real-life scenarios, the length of a system or object may also change due to external factors, such as temperature, pressure, or applied forces.

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