Calculating Triangle Side Length with Known Angles and Radius

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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

View attachment 8684
 
Attachments
  • Diagram of a pipe elbow bend in green with construction lines: radius r marked along the inner and outer edges, angle B at the outer corner, a right angle C marked at the bend centre, and length a marked in red.
    piep45m.jpg
    25.1 KB · Views: 156
  • Diagram of a pipe elbow bend in green with red construction lines: a right-angle triangle with sides labelled a and r, angle C marked at the corner, and blue radius lines labelled r and angle B at the bend centre.
    pipe75m.jpg
    28.6 KB · Views: 160
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)