find the number of radians in the central angle that subtends an arc of 6m on a circle of diameter 5m
θ = s/r = (6 m)/(5/2 m) = 12/5 radians = 2.4 radians
r = s/θ = (60 ft)/(3π/2) = 40/π ft ≅ 12.732 ft
θ = s/r = (6 m)/(5/2 m)
(6/1)(2/5)= 12/5 (2.4)
= 2.4 radians
To find the number of radians in the central angle that subtends an arc of 6m on a circle of diameter 5m, we can use the formula:
Arc Length = Radius × Central Angle
Given that the diameter is 5m, the radius is half of the diameter, which is 2.5m. The arc length is given as 6m.
Plugging these values into the formula:
6m = 2.5m × Central Angle
Simplifying the equation:
Central Angle = 6m / 2.5m
Central Angle = 2.4 radians
Therefore, the number of radians in the central angle that subtends an arc of 6m on a circle of diameter 5m is approximately 2.4 radians.
To find the number of radians in a central angle that subtends an arc, you need to use the formula:
radians = arc length / radius
In this case, the arc length is given as 6m, and the radius is half of the diameter, which is 5m/2 = 2.5m.
Substituting these values into the formula, we get:
radians = 6m / 2.5m = 2.4 radians
Therefore, the central angle that subtends an arc of 6m on a circle of diameter 5m is 2.4 radians.