contestada

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°

Respuesta :

TaeKwonDoIsDead

Answer:

C

Step-by-step explanation:

The formula we use here is:

Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex]  is the central angle

r is the radius

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

[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]

rounded to nearest degree, we have 46 degree

C is the right answer.

carlosego

Answer: OPTION C

Step-by-step explanation:

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

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

[tex]\theta=\frac{s}{r}[/tex]

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;

[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]

Convert to degrees:

[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°

Otras preguntas