MHB Derive a Generalised Formula for c-d with Respect to θ

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In the discussion, the relationship between the sides of a right triangle is explored, specifically focusing on the projection of side b, denoted as d, in relation to the angle θ. It is established that when θ equals 0, side b equals side c, and when θ equals 90, side d equals 0. The goal is to derive a generalized formula for the difference c - d as a function of θ. The conversation emphasizes using trigonometric functions to express the ratio of d to b. A clear formula will help in understanding the geometric relationships in the triangle.
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In the above given triangle when θ = 0 then b=c
But when θ = 90 then d=0
Since d is the projection of b
How we can derive a generalised formula for d or c-d with respect to θ
Plese may kindly be elaborated
 

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Hello and welcome to MHB! (Wave)

Look at the right triangle, having side lengths $b,\,d,\,h$. Using a trigonometric function, what is the ratio of $d$ over $b$?
 

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