Answer:
[tex]AC=4.3\ in[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The triangle AOC is an isosceles triangle
OA=OC=5/2=2.5 in -----> the radius of the circle
∠AOC=180°-60°=120°
∠CAO=∠ACO=120°/2=60°
Applying the law of cosines find the length of the chord AC
[tex]AC^{2}=OA^{2}+OC^{2}-2(OA)(OC)cos(120\°)[/tex]
substitute
[tex]AC^{2}=2.5^{2}+2.5^{2}-2(2.5)(2.5)cos(120\°)[/tex]
[tex]AC^{2}=18.75[/tex]
[tex]AC=4.3\ in[/tex]
