Find the angle substended at the center of a circle, radius 6.2cm by an arc of length 12cm
angle in radians * 6.2 = 12
angle in radians = 12/6.2
angle in degrees = angle in radians * 180 deg / 3.14159 radians
To find the angle subtended at the center of a circle by an arc, we can use the following formula:
θ = (l / r) * 180°
Where:
θ is the angle subtended at the center (in degrees),
l is the length of the arc,
r is the radius of the circle.
In this case, the length of the arc is given as 12 cm and the radius of the circle is 6.2 cm.
Using the formula, we can substitute the values:
θ = (12 / 6.2) * 180°
θ ≈ 34.839°
Therefore, the angle subtended at the center of the circle by the arc of length 12 cm is approximately 34.839°.
To find the angle subtended at the center of a circle by an arc, you can use the formula:
θ = (L / r) × (180 / π),
where:
θ = angle in degrees,
L = length of the arc, and
r = radius of the circle.
In this case, the length of the arc is 12 cm, and the radius is 6.2 cm. Plugging these values into the formula, we can calculate the angle as follows:
θ = (12 / 6.2) × (180 / π)
≈ 1.935 × 57.2958
≈ 110.999 degrees.
Therefore, the angle subtended at the center of the circle by the given arc is approximately 111 degrees.