Answer:
Option c). 5 square root 3 over 2
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle AOC
we know that
m∠AOC+m∠BOC=180° ----> by supplementary angles
m∠BOC=60° ---> given value
m∠AOC+60°=180°
m∠AOC=180°-60°=120°
step 2
we know that
The triangle AOC is an isosceles triangle
OA=OC=2.5 in -----> the radius of the circle
m∠CAO=m∠OCA ----> base angle
we have that
2m∠CAO=180°-m∠AOC
2m∠CAO=180°-120°
m∠CAO=30°
step 3
Find the measure of the chord AC
we know that
Applying the law of sines in triangle AOC
sin(30°)/2.5=sin(120°)/AC
AC=(2.5)sin(120°)/sin(30°)
sin(30°)=1/2
AC=(2.5)sin(120°)/(1/2)
AC=(5)sin(120°)
Remember that
sin(120°)=sin(60°)
sin(60°)=√3/2
substitute
AC=(5√3)/2
5 square root 3 over 2
