MHB Calculating Triangle Side Length with Known Angles and Radius

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To calculate the length of side "a" in a triangle with known angles and radius "r," the formula used is a = r * tan(0.5 * B), where B is the known angle at the corner. The discussion includes examples with a 45-degree and a 75-degree corner. The provided formula effectively simplifies the calculation, making it accessible for users. Participants express gratitude for the clarity of the solution. This method proves to be straightforward for determining triangle side lengths based on the given parameters.
BrentK
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Hi there.
Can someone tell me how to calculate the length of "a", shown in these drawings?
"r" is the radius of the corner, so these 2 sides have the same length.
"C" is 90 deg
angle "B" is known (the angle of the corner)

Here are the diagrams. First example 45 degree corner, second example 75 deg corner.

Many thanks in advance for your help! (Nerd) ;)

View attachment 8683

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If I understand the problem correctly, the answer is $a = r\tan\bigl(\frac12B\bigr)$.
 
Thanks Opalg!
That works perfectly!
So easy... I was trying to hard (Dull)
 
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