The chord of the circle is 9 m, it contracts the arc at 600. Find the length of the arc and the area

| September 3, 2021 | education

The chord of the circle is 9 m, it contracts the arc at 600. Find the length of the arc and the area of the corresponding sector.

In the condition there is an error, instead of 600 degrees, most likely 60 degrees.

We calculate the length of the circle using the following formula:
L = π * r * α / 180, α = 60 is the angle between the radii r.
The area of ​​the sector is calculated by the formula:
S = L * r / 2.
The radius of the circle can be found from the triangle AOB, where O is the center of the circle, AB = L is the chord, AO = OB = r are the radii. Then AOB is isosceles, and since the angle at the vertex O is 60 degrees, the angles A = B = (180-60) / 2 = 60. This means that the triangle is equilateral, therefore, the radius of the circle is equal to the chord and is equal to 9 m.
Find the circumference and area of ​​the sector (π = 3.14):
L = π * r * α / 180 = 3.14 * 9 * 60/180 = 9.42 m.
S = L * r / 2 = 9.42 * 9/2 = 42.39 m ^ 2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.