Hello!
To find the length of the arc on a circle with a radius length of 16 feet, and is also intercepted by a 60 degree angle, we need to change it from degrees to radians, and then multiply it by 16 feet, which is the radius.
To change from degrees to radians, we will to multiply it by π/180.
60 × π/180 = π/3 rad
Now, we multiply π/3 rad by 16 feet.
π/3 × 16 = 16π/3
This answer would be exact, but we are needed to substitute π for 3.14.
16(3.14)/3 = 16.75
Therefore, the length of the arc is equal to about 16.75.
The length of the arc on a circle with radius 16 ft intercepted by a 60° angle is 16.75 ft
learnt of an arc = ∅ / 360 × 2πr
where
∅ = 60°
r = radius = 16 ft
π = 3.14
Therefore,
length of an arc = 60 / 360 × 2 × 3.14 × 16
length of an arc = 1 / 6 × 100.48
length of an arc = 100.48 / 6
length of an arc = 16.7466667
length of the arc ≈ 16.75 ft
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