(b) what angle does an arc 5.5cm in length subtends at the centre of length subtend at the centre of a circle of radius 1/2m?
s = rθ
5.5 = 50 θ
90
To find the angle that an arc subtends at the center of a circle, you can use the formula:
Angle = (Arc Length / Radius) * 360 degrees
Given that the arc length is 5.5cm and the radius is 1/2 m, we need to convert the units so they are consistent.
1/2 m = 500 cm (since 1 meter equals 100 centimeters)
Now we can substitute these values into the formula:
Angle = (5.5 cm / 500 cm) * 360 degrees
Simplifying, we get:
Angle = (0.011) * 360 degrees
Angle ≈ 3.96 degrees
Therefore, the angle that the arc subtends at the center of the circle is approximately 3.96 degrees.
To find the angle that an arc subtends at the center of a circle, you can use the formula:
θ = s/r
where:
θ is the angle subtended by the arc,
s is the length of the arc, and
r is the radius of the circle.
In this case, the length of the arc is given as 5.5 cm, and the radius of the circle is given as 1/2 m.
First, let's convert the radius from meters to centimeters:
1/2 m = 0.5 m = 0.5 * 100 cm = 50 cm
Now, substitute the values into the formula:
θ = 5.5 cm / 50 cm
Now, divide 5.5 cm by 50 cm:
θ ≈ 0.11 radians
Therefore, the angle that the arc subtends at the center of the circle is approximately 0.11 radians.