To find the length of the chord, we first need to find the radius of the circle.
The formula for the area of a sector of a circle is given by:
Area = (θ/360)πr^2
Where θ is the central angle in degrees, r is the radius of the circle.
Given that the area of the sector is 32π cm^2 and the central angle is 210 degrees, we have:
32π = (210/360)πr^2
Solving for r, we get:
r^2 = (32*360)/(210)
r^2 = 55.4286
r ≈ √55.4286
r ≈ 7.451
Now, we can find the length of the chord using the formula:
Chord length = 2r sin(θ/2)
Chord length = 2*7.451 * sin(210/2)
Chord length ≈ 2*7.451 * sin(105)
Chord length ≈ 2*7.451 * 0.9659
Chord length ≈ 14.902 * 0.9659
Chord length ≈ 14.398 cm
Therefore, the length of the chord that subtends the angle of 210 degrees is approximately 14.398 cm.
A sector of a circle has an area of 32πcm^2 and contains a central angle of 210 degrees.calculate the length of the cord that subtends the angle given above
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