To find the radian measure of a central angle in a circle, we can use the relationship between the arc length, the radius, and the angle measured in radians. The formula to calculate the angle in radians (θ) is given by:
θ = s / r
Where:
- θ is the angle in radians.
- s is the length of the arc intercepted by the angle.
- r is the radius of the circle.
In this specific case, the radius (r) of the circle is 90 inches, and the arc length (s) is 130 inches. Plugging in the values:
- r = 90 inches
- s = 130 inches
Now substituting these values into the formula:
θ = 130 / 90
Calculating the fraction:
θ = 1.4444…
Thus, the measure of the central angle θ in radians for the given circle is approximately 1.44 radians.
In conclusion, if you want to find the radian measure of the central angle of a circle with a radius of 90 inches that intercepts an arc of length 130 inches, the answer is approximately 1.44 radians.