Calculate the angle at the centre of a circle subtended by a chord 6cm from the centre of the circle of radius 10m
To calculate the angle at the center of a circle subtended by a chord, we can use the following formula:
θ = 2 * arcsin(c / 2r)
where:
- θ is the angle at the center of the circle
- c is the length of the chord
- r is the radius of the circle
In this case, the length of the chord (c) is given as 6 cm and the radius of the circle (r) is given as 10 m. Since the units are different, we need to convert the length of the chord into meters:
6 cm = 6 / 100 m = 0.06 m
Now we can substitute the values into the formula:
θ = 2 * arcsin(0.06 / (2 * 10))
Calculating the value inside the arcsin function first:
θ = 2 * arcsin(0.003)
Using a calculator, the arcsin(0.003) is approximately 0.172 degrees.
Now we can substitute this value into the formula:
θ = 2 * 0.172
θ = 0.344 degrees
Therefore, the angle at the center of the circle subtended by the chord is approximately 0.344 degrees.