θ = 70°, d = 20 m
How do you find the length of the arc that subtends the given central angle θ on a circle of diameter d. (to two decimal places)
r = 10
so the whole circumference = 20π m
so your arc would be 70/360 of that
To find the length of the arc that subtends the given central angle θ on a circle of diameter d, you can use the formula:
Arc length = (θ / 360°) × π × d
Let's plug in the values given in the question:
θ = 70°
d = 20 m
Substituting these values into the formula, we have:
Arc length = (70° / 360°) × π × 20 m
Simplifying this expression:
Arc length = (0.1944) × π × 20 m
Now, to approximate the arc length to two decimal places, we can multiply the result by 20 and then round to two decimal places.
Arc length ≈ 12.28 m
Therefore, the length of the arc that subtends the central angle θ = 70° on a circle with diameter d = 20 m is approximately 12.28 meters.