Calculating Triangle Side Length with Known Angles and Radius

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SUMMARY

The discussion focuses on calculating the length of side "a" in a triangle with known angles and a radius "r". The formula established for this calculation is \( a = r \tan\left(\frac{1}{2}B\right) \), where angle "B" is the known corner angle and "C" is a right angle (90 degrees). Two specific examples provided include a 45-degree corner and a 75-degree corner, demonstrating the application of the formula effectively. The solution was confirmed by user Opalg, highlighting its simplicity.

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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
 

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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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