Find the length of a 40 degree arc in a circle with a radius of 4.

Question

anonymous · Answer

$$len = 2 \Pi r * (40/360)$$

shayaan_mustafa · Answer

use formula of arc length.
$$\large s=r \theta$$

shayaan_mustafa · Answer

@fractal5 
2*pi*r is the circumference of the circle. I think it is just for arc length.

anonymous · Answer

Can you explain more please?

anonymous · Answer

@Shayaan_Mustafa multiplying the circumference by the part of the arc, that is 40 deg should give the length of that arc

shayaan_mustafa · Answer

oh yes. you did so. sorry i just saw 2*pi

anonymous · Answer

@Brooke_Tessa_Savoie if you know the circumference of the circle, which is like an arc of 360 deg, you can find the length of arc given the angle. Hope that makes sense

shayaan_mustafa · Answer

@Brooke_Tessa_Savoie http://www.mathwarehouse.com/trigonometry/radians/s=r-theta-formula-equation.php

shayaan_mustafa · Answer

remember in s=r*theta.
theta is in radians.

anonymous · Answer

I dont know the circumference..

shayaan_mustafa · Answer

actually you are given with a part of the circumference. and that small part is known as arc.

anonymous · Answer

You have to find the circumference from the radius C=2Πr

anonymous · Answer

okay thanks. so the circum=25.12
so 25.12 ( 40/360) ?

anonymous · Answer

so Now how do I finish solving it?

anonymous · Answer

yep

anonymous · Answer

just do the math answer = 25.12 * (40 / 360 )

anonymous · Answer

And how did you get 360?

anonymous · Answer

because the angle inside a circle is 360 deg, and you just want to find the length of the arc of 40 deg, you basically find the ratio of the arc angle to the whole circle, and multiply by circumference

anonymous · Answer

It's like cross multiplication
If 360 deg gives you 25.12
how much will 40 give you

anonymous · Answer

Okay Im lost and confused.

anonymous · Answer

40º is 0.7 rad aproximatly
so arc length is 0,7*4 = 2.8

anonymous · Answer

How did you figure out that 40 is 0.7 rad?

anonymous · Answer

you can mesure angle in degrees or in radians. (Radian is a mesure system where radius of a circle is taken like unit length) It is known that 360º = 2Pi radians
So if you have fraction of 360º   (40º/360º) it should be same for any type of mesuring system you choose, since you mesure same angle so 40º/360º = x/2Pi from here
x=2Pi( 40º/360º) is a angle of 40º given in radians

anonymous · Answer

Okay well how do you solve it?

anonymous · Answer

after you have you angle in radians, just multiply it by radius length.

anonymous · Answer

The answer is 2.79