Determine Chord

There are 2 exercises on this page:

For this first exercise we will determine the CHORD (line “BC”) of an arc if we know the RISE “AD” and the RADIUS.

Our radius Radius will be 96 inches and the Rise (line “AD”) will be 24 inches.
96 – 24 = 72 Now 96 ² – 72 ² = 4032. Now (square-root) you get 63.5″
Now x 2 = 127 inches.
The CHORD of this arc is 127 inches.

In Short:
Radius – Rise = X   Radius² – X² = ___ √  ___ x 2 = CHORD

This exercise is good for all angles of less than 180 degrees of arc.

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In this second exercise, we will determine the CHORD of an arc, if we know the RADIUS and the ARC LENGTH.

This exercise is useful when Rolling Rings of less than 180 degrees of arc.

Our Radius will be 120” and the Arc Length will be 288”.

Punch in 120” x  = you get 376.99

Now 376.99 ÷ 288 = you get 1.309.

Now hit the 1/X key, you get .7639.

Now x 180 = you get 137.51 Now divide by 2 = 68.755

Punch SIN you get .932 now x 120” = 111.845

Now 111.845 x 2 =223.69”     

Your CHORD is 223.69”

 In Short:

Radius x  = ____  ÷  Arc Length = ____ 1/X x 180 = Angle

÷ 2 = ____  SIN ____ x Radius =  ____ x 2 = CHORD