Question
- The length of an arc is 18 cm and the radius of the circle is
6 cm . What is the radian measure of the central angle?
6 cm . What is the radian measure of the central angle?
Ask by Chadwick Klein. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The radian measure of the central angle is 3 radians.
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Beyond the Answer
To find the radian measure of the central angle, you can use the formula for the arc length, which is
, where
is the arc length,
is the radius, and
is the central angle in radians. Plugging in the values you have:
.
From this, you can solve for
by dividing both sides by 6, giving you
radians. So, the central angle measures 3 radians!
If you want to convert this to degrees, you can use the conversion factor
. Multiplying
radians by
gives you
degrees, which is a fun little way to see the same angle from a different perspective!