Height of the arc - formula

Calculate the arc's height if the arc's length is 65 and the chord length is 33.
Does there exist a formula to solve this?

Correct answer:

h = 22.537

t = 33 s = 65 t = 2 r sin α / 2 s = α r t = 2 \cdot (s / α) \cdot sin α / 2 α = 2 \cdot (s / t) \cdot sin α / 2 α (n + 1) = 2 \cdot (s / t) \cdot sin (α (n) / 2) α (n + 1) = 3.9394 \cdot sin (α (n) / 2) α_{0} = 1.5707963267949 = 90 °; r = 41.380285203893; h = 12.12 α_{1} = 2.7855721683106 = 159 ° 3 6^{'} 6 "; r = 23.334523779156; h = 19.203 α_{397} = 3.7553499087454 = 215 ° 9^{'} 57 "; r = 17.308640094663; h = 22.537 α_{398} = 3.7553499087454 = 215 ° 9^{'} 57 "; r = 17.308640094663; h = 22.537 α_{399} = 3.7553499087454 = 215 ° 9^{'} 57 "; r = 17.308640094663; h = 22.537 α = 3.7553499087454 ≐ 215 ° 9^{'} 57 " r = 65 / α = 17.308640094663 h = r (1 - cos α / 2) h = 22.537

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