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given the circumference of circle b is 85 ft . what is the arc lenght of arc ADC?and the lenght of arc Ac​

given the circumference of circle b is 85 ft . what is the arc lenght of arc ADC?and-example-1
User Amoy
by
2.9k points

1 Answer

19 votes
19 votes

Answer:

Length of arc AC = 10.6 ft

Length of arc ADC = 73.4 ft

Explanation:

θ = 45°

Circumference = 85 ft

✔️First, find the radius:

Circumference of a circle = 2πr

Thus:

85 = 2πr

Solve for r

Use 3.14 as π

Divide both sides by 2π

85/2π = r

85/2*3.14 = r

85/6.28 = r

r = 13.5350318 ≈ 13.5 ft (nearest tenth)

✔️Find length of arc ADC:

Length of arc = θ/360 × Circumference of the circle

θ = 360 - 45° = 315°

Circumference = 85 ft

Plug in the values

Length of arc ADC = 315/360 × 85

= 74.375 ≈ 73.4 ft (nearest tenth)

✔️Find length of arc AD:

Length of arc = θ/360 × Circumference of the circle

θ = 45°

Circumference = 85 ft

Plug in the values

Length of arc AC = 45/360 × 85

= 10.625 ≈ 10.6 ft (nearest tenth)

User Bradjive
by
2.7k points
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