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Answer to Question #25177 in Trigonometry for Alec Barger

Question #25177
Sheldon designed a pizza cutter that allows independently setting
the cut angle for each slice. This permits equitable slicing when toppings are
arranged inequitably. Two slices are to be cut from a 16 inch diameter pizza.
On the right side, the
toppings cover most of the
crust. A skinny band of
uncovered crust at the
outer radius averages ½
inch.
On the left side, the
uncovered band averages 1
inch.
a) The left side slice was cut first with a 45o (π/4) angle. Sheldon calculated a
smaller cut angle for the right side slice to ensure that the toppings areas are
the same. What is that angle in radians? (3 digits of accuracy)
b) Suppose that the right side slice was cut first with a 36o (π/5) angle.
Sheldon then calculated a larger cut angle for the right side slice to ensure
that the toppings areas are the same. What is that angle in radians? (3 digits
of accuracy)
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