Question

The length of an intercepted arc of a central angle of a circle is 4 cm. If the radius of the circle is 5 cm, what is the measurement of the central angle to the nearest whole degree?

A) 35°
B) 41°
C) 46°
D) 50°

Answer 1

Answer: OPTION C

Explanation:

To solve this problem you must apply the proccedure shown below:

- Use the following formula for calculate the measure fo the central angle:

`\theta=(s)/(r)`

Where s is the arc length and r is the radius.

- Know the lenght of the arc and the radius, you can substitute values.

Therefore, you obtain;

`\theta=(4)/(5)=0.8\ radians`

Convert to degrees:

`((0.8)(180\°))/(\pi)=45.83\°`≈46°

Answer 2

C

Explanation:

The formula we use here is:

Length of arc =
`(\theta)/(360)*2\pi r`

Where

`\theta` is the central angle

r is the radius

Putting the given information into the formula we can solve for the central angle:

`LengthOfArc=(\theta)/(360)*2\pi r\\4=(\theta)/(360)*2\pi(5)\\4=(\theta)/(360)*10\pi\\(4)/(10\pi)=(\theta)/(360)\\\theta=(4*360)/(10\pi)\\\theta=45.84`

rounded to nearest degree, we have 46 degree

C is the right answer.