Ab id a diameter of a circle centered at o. c is a point on the circle such that angle boc is 60 degrees. if the diameter of the circle is 5 inches the length of the chord ac expressed in inches is
a.3
b. 5 square root 2 over 2
c.5 square root 3 over 2
d. 3 square root 3
e. none of the above

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

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