Answer: 59.690260418206
The result is approximate. Round that value however you need to.
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Step-by-step explanation:
For a circle with radius r = 142.5, the full distance around the edge (aka perimeter aka circumference) is found by using the formula below.
C = 2*pi*r
C = 2*pi*142.5
C = 895.353906273091
That value is approximate. I used my calculator's stored value of pi to get the most accuracy possible.
That value of roughly 895 represents the distance around a full circle of that radius, but we only want a 24 degree pizza slice.
In other words, we want 24/360 = 1/15 of the full perimeter
(1/15)*895.353906273091 = 59.690260418206