An arc of lenght 28m subtends an angle of 24 at the centre of a circle.In the same circle,what angles does an arc of lenght 35m subtend?
arc length is proportional to the angle.
So you have proportion
θ/35 = 24/28
What angle does an arc 5.5cm in length subtends at the centre of a circle of radius 1/2m?
To find the angle subtended by an arc of length 35m in the same circle, we can use the concept of the angle subtended by a chord in a circle.
The ratio of the lengths of two arcs subtended by the same angle at the center of a circle is equal to the ratio of the lengths of the corresponding chords.
Let's denote the angle subtended by the arc of length 28m as θ1, and the angle subtended by the arc of length 35m as θ2.
Since the ratio of the lengths of the arcs is equal to the ratio of the lengths of the corresponding chords, we can write:
28/35 = chord length corresponding to θ1 / chord length corresponding to θ2
We can simplify this equation by cross-multiplying:
28 * chord length corresponding to θ2 = 35 * chord length corresponding to θ1
We know that for any given angle, the length of the chord is directly proportional to the length of the arc. Therefore, we can write:
chord length corresponding to θ1 = length of arc subtended by θ1 = 28m
chord length corresponding to θ2 = length of arc subtended by θ2 = 35m
Substituting these values into the equation, we get:
28 * 35 = 35 * 28
This equation simplifies to:
980 = 980
This means that the angle subtended by the arc of length 35m is the same as the angle subtended by the arc of length 28m, which is 24 degrees.
So, the arc of length 35m subtends an angle of 24 degrees at the center of the circle.
To find the angle that an arc subtends in a circle, we can use the formula:
Angle = (Arc length / Circle circumference) * 360 degrees
Let's calculate the angle subtended by the arc of length 28m first:
Circle circumference = 2 * π * radius
Since we don't have the radius information, we can use a different approach. We know that the angle at the center of the circle is 24 degrees, and the arc length is 28m. From this information, we can set up a proportion:
Angle in degrees / 360 degrees = Arc length / Circle circumference
Plugging in the known values:
24 degrees / 360 degrees = 28m / Circle circumference
Now, solving for the Circle circumference:
Circle circumference = (28m * 360 degrees) / 24 degrees
= 420m
So, the circumference of the circle is 420m.
Now, let's find the angle subtended by the arc of length 35m:
Angle = (Arc length / Circle circumference) * 360 degrees
= (35m / 420m) * 360 degrees
= (1/12) * 360 degrees
= 30 degrees
Therefore, an arc of length 35m subtends an angle of 30 degrees in the same circle.