Question
An arc 33cm long subtends a central angle of a circle with a radius of 16m. Determine the measure of the central angle in radians.
Answers
GPT 3.5
To find the measure of the central angle in radians, we first need to convert the arc length to meters (since the radius is measured in meters).
1 cm is equal to 0.01 meters, so 33 cm is equal to 0.33 meters.
Now, we can use the formula for calculating the central angle in radians:
θ = s / r
where θ is the central angle in radians, s is the arc length, and r is the radius of the circle.
Plugging in the values we have:
θ = 0.33 m / 16 m
θ = 0.020625 radians
Therefore, the measure of the central angle in radians is approximately 0.0206 radians.
1 cm is equal to 0.01 meters, so 33 cm is equal to 0.33 meters.
Now, we can use the formula for calculating the central angle in radians:
θ = s / r
where θ is the central angle in radians, s is the arc length, and r is the radius of the circle.
Plugging in the values we have:
θ = 0.33 m / 16 m
θ = 0.020625 radians
Therefore, the measure of the central angle in radians is approximately 0.0206 radians.