Question

An arc of length 10 meters is formed by a central angle A on a circle of radius 4. The measure of A in degrees (to two decimal places) is _____. A. 143.24 B. 2.50 C. 216.76 D. 36.76

Answer 1

the length of an arc in a circle is radius x the angle (Ф).

Mind you angle Ф should be in radian.
In our case we have the arc length & the radius, find the angle (Ф)
Arc Length = Ф x 4 = 10 meters ===> Ф=10/4 =5/2 = 2.5 RADIANS

Now let's convert 2.5 RADIANS into DEGREE:
2.5/π = x/180 ===> x= (2.5 x 180) / π ==>143.239° or 143.24° (A)

Answer 2

A) 143.24

Explanation:

Here we have to use arc length of a circle formula.

Arc length =
`((Central angle)/(360) )*2*pi*r`

From this formula, we can drive central angle.

Central angle = (Arc length *360)/2πr

Given: Arc length = 10; r =4 and π = 3.14159

Plug in the given values in the above formula, we get

Central angle =
`(10*360)/(2*3.14159*4)`

= 3600/25.13

Central angle = 143.24

Therefore, answer A) 143.24