An arc of length 28cm subtend an angle of 24° at the center of the circle. In the same circle what does an arc of 35cm subtend
answer the question
answer the question.
To find out what angle an arc of 35 cm subtends at the center of a circle, we can use the formula:
Angle = (Arc Length / Circumference) x 360°
First, let's calculate the circumference of the circle using the given information.
The arc of length 28 cm subtends an angle of 24° at the center of the circle. Using the formula mentioned above, we can set up the equation:
24° = (28 cm / Circumference) x 360°
To solve for the circumference, we rearrange the equation:
Circumference = (28 cm / 24°) x 360°
Next, we can substitute the values and calculate the circumference:
Circumference = (28 cm / 24°) x 360°
Circumference = 420 cm
Now that we know the circumference of the circle is 420 cm, we can determine the angle subtended by an arc of 35 cm using the same formula:
Angle = (35 cm / 420 cm) x 360°
Calculating the angle:
Angle = (35 cm / 420 cm) x 360°
Angle ≈ 30°
Therefore, an arc of 35 cm subtends an angle of approximately 30° at the center of the circle.
Since arc length is a linear unit, set up a simple proportion
arc/35 = 28/24
arc = 35(28/24) = ....