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

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SUMMARY

The discussion focuses on finding the distance d(x) without utilizing trigonometry or calculus. The initial approach involved using the angle A, defined as arctan(5/4), and applying the law of cosines. However, participants suggest an alternative method by dropping a perpendicular from point C to line AB, utilizing similar triangle arguments and the Pythagorean theorem to establish a relationship between x and d.

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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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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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Cheers, solution followed readily.
 

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