Question

An arc of length 12 meters is formed by a central angle A on a circle of radius 9. The measure of A in degrees is what? 42.97 1.30 8.38 76.39

Answer 1

arc/(2πr)=α/360

α=360*arc/(2πr)

α=180*arc/(πr), since arc=12 and r=12

α=2160/(9π)°

α=240/π°

α≈76.39° (to nearest one-hundredth of a degree)

Answer 2

Option 4th is correct

76.39 degree

Explanation:

The arc length(l) is given by:

`l =r \theta` .....[1]

where, r is the radius of the circle and
`\theta` is the central angle in radian

As per the statement:

An arc of length 12 meters is formed by a central angle A on a circle of radius 9

⇒l = 12 meters and r = 9 meter

substitute the given values in [1] we have;

`12 = 9A`

Divide both sides by 9 we have;

`(12)/(9) =A`

Use conversion:

1 radian = 57.2958 degree

then;

`(12)/(9)` radian = 76.3943998 degree.

⇒
`A = 76.39^(\circ)`

Therefore, the measure of angle A in degree is, 76.39