find, to the nearest tenth of a meter, the length of the arc intercepted by a central angle of 160 degrees if a radius of the circle in 8 meters long
(160/180)*pi*R = 22.3 meters
Convert 160 degrees to radians (by multiplying by pi/180 radians per degree) and multiply the result by R.
To find the length of the arc intercepted by a central angle of 160 degrees, we can use the formula:
Arc Length = (Central Angle / 360 degrees) x (2π × Radius)
Given that the central angle is 160 degrees and the radius is 8 meters, we can substitute these values into the formula:
Arc Length = (160 degrees / 360 degrees) x (2π × 8 meters)
First, let's calculate the value of (160 degrees / 360 degrees):
160 degrees / 360 degrees = 0.4444 (rounded to four decimal places)
Next, let's substitute this value and the value of the radius into the formula:
Arc Length = 0.4444 x (2π × 8 meters) = 0.4444 x (16π meters)
Finally, let's calculate the approximate value of the arc length by multiplying:
Arc Length ≈ 7.0224π meters
To find the answer to the nearest tenth of a meter, we need to evaluate π (pi) as approximately 3.14:
Arc Length ≈ 7.0224 × 3.14 meters
Arc Length ≈ 22.05 meters (rounded to the nearest tenth of a meter)
Therefore, the length of the arc intercepted by a central angle of 160 degrees in a circle with a radius of 8 meters is approximately 22.1 meters to the nearest tenth of a meter.