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

[1MileCrash]

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?

 

[gopher_p]

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.

 

[1MileCrash]

Cheers, solution followed readily.