Question

Question
1
Question
2
A)
To derive the fact that the length of the arc of a circle intercepted by an angle is proportional to theradius of the circle, what should the arc length first be compared to?
(1 point)
a chord
the circumference
the diameter
the area
A)
If the arc of a circle is 15 meters long and the radius of the circle is 3 meters, then what is themeasure of the central angle, to the nearest tenth of a degree, that intercepts that 15-meter arc?
(1 point)
286.5 degrees
282.7 degrees
353.4 degrees
7.9 degrees
Question
3
Question
4
A)
The measure of an angle in radians is the ratio of the arc length created by the angle to the circle’sradius. If the radius is 6 feet and the arc length is
, then define the angle measure in radians.
(1 point)
2π
6
π
3
π
12
π
π
3
A)
If the radius of a circle is 10 feet and the central angle is
, then what is the arc length in radians?
(1 point)
3π
4
30
π
60
π
15
π
2
15
π
Question
5
A)
If a central angle of
is created with two radii that are 30 inches long, then how long is the arc theywill cut in radians?
(1 point)
5π
3
15
π
5
π
18
50
π
π
2

Answer 1

Here are the answers with brief work:

1) To derive the proportionality you compare the arc length to the circumference.

2) s = 15 m, r = 3 m → θ (radians) = s/r = 15/3 = 5 rad. Convert to degrees: 5·180/π ≈ 286.5°. (Answer: 286.5°)

3–4) Using θ = s/r and s = r·θ:

- If r = 6 ft and s = 2π (assuming the missing arc length is 2π), then θ = s/r = 2π/6 = π/3.

- If r = 10 ft and θ = 3π/2 (assuming that is the missing central angle), then arc length s = r·θ = 10·(3π/2) = 15π.

5) If the central angle is 5π/3 and r = 30 in, then s = r·θ = 30·(5π/3) = 50π.

If any of the missing given values are different, tell me the exact arc/angle and I’ll recompute.