Given:
Given that the radius of the merry - go - round is 5 feet.
The arc length of AB is 4.5 feet.
We need to determine the measure of the minor arc AB.
Measure of the minor arc AB:
The measure of the minor arc AB can be determined using the formula,
[tex]Arc \ length=(\frac{\theta}{360})2 \pi r[/tex]
Substituting arc length = 4.5 and r = 5, we get;
[tex]4.5=(\frac{\theta}{360})2 (3.14)(5)[/tex]
Multiplying the terms, we get;
[tex]4.5=(\frac{\theta}{360})31.4[/tex]
Dividing, we get;
[tex]4.5=0.087 \theta[/tex]
Dividing both sides of the equation by 0.087, we get;
[tex]51.7=\theta[/tex]
Rounding off to the nearest degree, we have;
[tex]52=\theta[/tex]
Thus, the measure of the minor arc AB is 52°
