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

1 answer:

3 0

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

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