Question

Find the length of the chord of a circle of radius 100 feet subtended by an angle of 75◦ ?

Answer 1

1. By definition, the chord of a circle is a segment that joins the two points of an arch and if it passes through the center of the circle, is called "diameter". There is a formula that you can use to find the chord lenght. This is:

 Chord lenght=2rSin(A/2)

 2. Let's convert the angle from degrees to radians:

 75°π/180°=5π/12

 3. So, you have:

 r: It is the radius of the circle (r=100 feet).
 Sin: It is the sine function.
 A: It is the angle subtended at the center by the chord (A=5π/12).
 

 4. When you substitute these values into the formula (Chord lenght=2rSin(A/2)), you obtain the chord lenght:

 Chord lenght=2rSin(A/2)
 Chord lenght=2(200 feet)(Sin(5π/12/2))

 5. Therefore lenght of the chord is:
 Chord lenght=18.2706 feet