A strip of metal 58cm long is bent into an arc of a circle of radius 24cm calculate to the nearest degree the angle that the arc subtends at the centre of the circle
58 / (2 * π * 24) = a / 360º
To find the angle that the arc subtends at the center of the circle, we can use the formula:
θ = (s / r) * (180 / π)
Where:
θ - the angle in degrees
s - the length of the arc
r - the radius of the circle
π - Pi, approximately 3.14159
In this case, we have:
s = 58 cm (length of the arc)
r = 24 cm (radius of the circle)
Plugging in the values, we can calculate the angle:
θ = (58 / 24) * (180 / π)
θ = (2.4167) * (57.2958)
θ ≈ 138.4875 degrees
Therefore, the angle that the arc subtends at the center of the circle is approximately 138.4875 degrees.