Drawn in a circle whose radius is 14 cm, chord AB is 18 cm long. Calculate the angular
size of minor arc AB.
Draw a diagram, where a radius bisects the chord. You will see that the arc is subtended by the angle θ, where
sin(θ/2) = 9/14
The arc length is then s = rθ
To calculate the angular size of a minor arc, we need to use the formula:
Angle = (Arc Length / Circle Circumference) * 360 degrees
First, let's find the circumference of the circle with a radius of 14 cm using the formula:
Circumference = 2 * π * radius
Circumference = 2 * 3.14 * 14 cm
Circumference = 87.92 cm
Now, we can calculate the angular size of the minor arc AB using the arc length (18 cm) and the circle's circumference:
Angle = (18 cm / 87.92 cm) * 360 degrees
Angle = 0.205 * 360 degrees
Angle ≈ 73.8 degrees
Therefore, the angular size of minor arc AB is approximately 73.8 degrees.