Question

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Answer 1

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

What is the measure of the central angle of a circular section?

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π)     (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

To learn more on subtended angles: brainly.com/question/17158173

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