How can I show that when r >> d, R1 - R2 is approximately equal to d cos theta? This was an intermediate step in my physics book when they derived some formula, and it just drives me crazy that I can't figure this out!

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- Mar 15th 2013, 02:10 PMgralla55Approximating difference between sides of triangle
How can I show that when r >> d, R1 - R2 is approximately equal to d cos theta? This was an intermediate step in my physics book when they derived some formula, and it just drives me crazy that I can't figure this out!

- Mar 15th 2013, 02:45 PMShakarriRe: Approximating difference between sides of triangle
Using the cosine rule for the triangle on the right hand side

And using the cosine rule on the triangle on the left side

cos180= -1, sin180=0

As r becomes much larger than d R1 and R2 become nearly equal to r