To find the radian measure of the central angle in a circle, we can use the formula:
θ = s / r
Where:
- θ is the central angle in radians.
- s is the length of the arc.
- r is the radius of the circle.
In this case, we have:
- s = 130 inches
- r = 90 inches
Now, we can substitute these values into the formula:
θ = 130 / 90
When we calculate this, we get:
θ = 1.444 radians
This result means that the central angle that intercepts an arc of length 130 inches on a circle with a radius of 90 inches is approximately 1.444 radians.