What angle does an arc of 10cm subtend at the centre of a circle of radius 10cm? Give the answer to the nearest 0.1
simple way:
arc-length = rθ , where θ is the sector angle in radians
10 = 10θ
θ = 1 radian
detailed solution:
circumference of whole circle = 2π(10) = 20π cm
so by ratios
sector arc : circumference = sector angle : whole rotation
10/20π = θ/2π
1/2 = θ/2
θ = 1
To find the angle that an arc subtends at the center of a circle, we can use the formula:
θ = (s / r) * 180 / π
Where:
θ is the angle in degrees,
s is the length of the arc,
r is the radius of the circle, and
π is a mathematical constant approximately equal to 3.14159.
Given that the radius (r) of the circle is 10 cm and the length of the arc (s) is also 10 cm, we can substitute these values into the formula:
θ = (10 / 10) * 180 / π
Simplifying this expression:
θ = 1 * 180 / π
To determine the value in degrees, we can substitute the approximate value of π as 3.14159:
θ = 180 / 3.14159
Calculating this expression:
θ ≈ 57.29578 degrees
Therefore, the angle that the given arc subtends at the center of the circle is approximately 57.3 degrees (rounded to the nearest 0.1).
To find the angle that an arc subtends at the center of a circle, you can use the formula:
Angle = (Arc length / Radius) * (180° / π)
Given that the radius of the circle is 10 cm and the arc length is also 10 cm, we can substitute these values into the formula to find the angle:
Angle = (10 cm / 10 cm) * (180° / π)
= 1 * (180° / π)
≈ 57.3° (rounded to the nearest 0.1)
Therefore, the angle that the arc of 10 cm subtends at the center of a circle with a radius of 10 cm is approximately 57.3 degrees.