Calculate the radius of segment of length20cm which subtend at angle 120 degree leave your answer to the nearest whole number take pie 22/7
when you say a segment of length 20, is that the chord length or the arc length?
in any case, se the related problems below.
120° / 360° = 120° ∙ 1 / 120° ∙ 3 = 1 / 3
The circumference of circle:
C = 2 r π
Segment which subtend at angle 120° have lenght of one third of circumference.
C / 3 = 20 cm
2 r π / 3 = 20
Multiply both sides by 3
2 r π = 60
Divide both sides by 2 π
r = 60 / 2 π
r = 30 / π = 30 / ( 22 / 7 ) = 30 ∙ 7 / 22 = 210 / 22 = 9.5454...
r = 10 cm
rounded to the nearest whole number
Your question is ambiguous.
Bosnian assumed that the 20 cm referred to the arc length.
This assumption makes sense, since you mention using π.
One could also assume that the 20 cm refers to the length
of the chord, if so ....
simplest way:
you have an isosceles triangle with base angles of 30° each .
By the sine law:
r/sin30 = 20/sin120
r = 20sin30/sin120 = appr 11.55 cm
btw, this is 2022. If your text suggests using 22/7 for π, it is time to
replace that medieval text. Every decent calculator has the value of
π installed as a constant.
To find the radius of a segment, you can utilize the formula for the length of an arc. The formula is:
Length of Arc = (θ/360) * 2πr
Where:
- θ is the central angle in degrees
- r is the radius of the circle
To find the radius of the segment, you need the angle subtended by the segment, which is given as 120 degrees, and the length of the segment, which is given as 20 cm.
First, plug the given values into the formula:
20 = (120/360) * 2 * 22/7 * r
Next, simplify and solve for r:
20 = (1/3) * (44/7) * r
Multiply both sides by 3 to eliminate the fraction:
60 = (44/7) * r
To isolate r, divide both sides by (44/7):
r = (60) / (44/7)
Now, simplify the expression on the right side:
r = (60) * (7/44)
r = 10/11
Therefore, the radius of the segment is approximately 0.91 cm when rounded to the nearest whole number.