How can we compute dx in terms of R and θ in this given right triangle?

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SUMMARY

The discussion focuses on deriving the expression for the differential length dx in a right triangle, specifically in terms of R and θ. The correct formula is established as dx = (R/cos² θ) dθ, which is confirmed by the solutions manual. The relationship between the triangle's legs and the angle θ is crucial for understanding how dx varies with changes in θ while R remains constant.

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Homework Statement


This is part of a find the electric field problem. I've narrowed down the part I find confusing.

Consider a right triangle, with legs of length x and R. Angle θ is opposite x. Leg x is a segment of a ray starting where lines x and R intersect. There is a differential length dx along line x (it is at a vertex of the right triangle). Find dx in terms of R and θ.

Homework Equations


standard trig functions, pythagorean theorem?

The Attempt at a Solution


The answer according to the solutions manual is dx = (R/cos^2 θ) dθ. Obviously, I cannot understand at all where that came from.

I did get R tan ( θ + dθ) = x + dx but that isn't very helpful either
 
Last edited:
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It sounds like R is fixed, while x and θ can vary.

Can you write an expression for x in terms of R and θ?
 

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