Fred works for $8.75 per hour. his regular hours are 40 hours per week and he gets time and a half for overtime. one week he works 47.5 hours. he wants to calculate his pay.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584