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

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The discussion focuses on deriving a generalized formula for the variable d in relation to c-d with respect to the angle θ in a right triangle. It establishes that when θ = 0, b equals c, and when θ = 90, d equals 0, indicating that d is the projection of b. The participants seek to clarify the relationship between these variables using trigonometric functions to express the ratio of d over b.

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View attachment 5681

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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