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.)

Convert units: To find the value of a, we need to use the relationship between radians and degrees. We know that 180 degrees is equal to pi radians. The problem states that a pi radians is equal to 900 degrees. We can set up a proportion to solve for a.Set up proportion: Using the proportion, we have a pi radians / pi radians = 900 degrees / 180 degrees. Simplifying the left side, we get a = 900 degrees / 180 degrees.Simplify proportion: Now we perform the division on the right side: a = 900 / 180. This simplifies to a = 5.Perform division: We have found the value of a to be 5. This means that 5 pi radians is equal to 900 degrees.

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

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Algebra 2

Convert between radians and degrees

Full solution

Q. If

a \pi

radians is equal to

900

degrees, what is the value of

a

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

Convert units: To find the value of $a$ , we need to use the relationship between radians and degrees. We know that $180$ degrees is equal to $\pi$ radians. The problem states that $a \pi$ radians is equal to $900$ degrees. We can set up a proportion to solve for $a$ .
Set up proportion: Using the proportion, we have $a \pi \text{ radians} / \pi \text{ radians} = 900 \text{ degrees} / 180 \text{ degrees}$ . Simplifying the left side, we get $a = 900 \text{ degrees} / 180 \text{ degrees}$ .
Simplify proportion: Now we perform the division on the right side: $a = \frac{900}{180}$ . This simplifies to $a = 5$ .
Perform division: We have found the value of $a$ to be $5$ . This means that $5 \pi$ radians is equal to $900$ degrees.