In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree

Question

inessss [21]

3 years ago

8

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree

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Mathematics

2 answers:

PIT_PIT [208] · Answer 1 · 2022-04-14T20:27:49+03:00

PIT_PIT [208]3 years ago

8 0

Answer:

Step-by-step explanation:

Length of a circular arc is given by:

S = rФ

where Ф is the angle in radians subtended at the center by the arc.

Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°

Measure of minor arc AB is 60°

Degger [83] · Answer 2 · 2022-04-14T18:02:33+03:00

The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.

In this case, the angle would be s/r or 4.2/4 which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.