Question

determine the length of a chord whose central angle is 75° in the circle with the radius of 12 inches. ​

Answer 1

Answer:

Step-by-step explanation:

other two sides joining center to the ends of chord=radius of circle=12 in

using cosine formula

$cos A=\frac{b^2+c^2-a^2}{2bc} \\2bc cos~A=b^2+c^2-a^2\\\angle A=75^\circ\\b=c=r=12~in\\2*12*12~cos~75=12^2+12^2-a^2\\a^2=2*12^2-2*12^2 cos ~75\\a^2=2*12^2(1-cos 75)\\a=12\sqrt{2(1-cos~75)} \approx 14.6~inches$