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If a pi radians is equal to 900 degrees, what is the value of a ? (The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2pi.)

If aπ a \pi radians is equal to 900900 degrees, what is the value of a a ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)

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Full solution

Q. If aπ a \pi radians is equal to 900900 degrees, what is the value of a a ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)
  1. Convert units: To find the value of aa, we need to use the relationship between radians and degrees. We know that 180180 degrees is equal to π\pi radians. The problem states that aπa \pi radians is equal to 900900 degrees. We can set up a proportion to solve for aa.
  2. Set up proportion: Using the proportion, we have aπ radians/π radians=900 degrees/180 degreesa \pi \text{ radians} / \pi \text{ radians} = 900 \text{ degrees} / 180 \text{ degrees}. Simplifying the left side, we get a=900 degrees/180 degreesa = 900 \text{ degrees} / 180 \text{ degrees}.
  3. Simplify proportion: Now we perform the division on the right side: a=900180a = \frac{900}{180}. This simplifies to a=5a = 5.
  4. Perform division: We have found the value of aa to be 55. This means that 5π5 \pi radians is equal to 900900 degrees.

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