Atriangle oab is formed where o is the centre of a cricle of radius 12cm, and a and b are endpoints of a 15cm chord. find the angle subtended at the centre of the circle, in degrees and minutes

We are asked to solve for the angle AOB and we are given with the following values:
radius = 12 cm
length of AB = 15 cm

We can solve for angle AOC such as shown below:
sin AOC = opposite/hypotenuse
sin AOC = 7.5/12
∠AOC =38.68°

The angle subtended at the center of the circle is just twice of ∠AOC, then we have:
∠AOB = 38.68° x 2
∠AOB = 77.36°

The answer is 77° 21' 51.75".