Question

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

Answer 1

Explanation:

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

using cosine formula

`cos A=(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√(2(1-cos~75)) \approx 14.6~inches`