Question

A central angle of a circle of radius 50 cm intercept an arc of 10cm . Express the central angle in radian and in degree

Answer 1

Step-by-step explanation:

Here we have given ,

radius(r)=50cm and(arc ) S = 10cm

Let Φ^c be the angle subtended by the arc at the centre of the circle.

Then, S = r .Φ

∴ 10 = 50 . Φ

∴ Φ = ( 10 / 50)

∴ Φ = ( 1 / 5)^c

Now, 1^c = ( 180 / π )°

∴ (1/5 )=((1 /5 )x(180/π ))°= (36/π)°

Φ in degree ⤵

∴Φ = ( 36 / π )°

Φ in redians ⤵

∴Φ = ( 1/5 )^c

∴ required angle in radian or in degree = ( 1/5)^c or ( 36 /π )°

Answer 2

» A central angle of a circle of radius 50 cm intercept an arc of 10cm.

Here..

r (radius) = 50 cm

l (length of arc) = 10 cm

__________ [GIVEN]

• We have to find the central angle (Ø) of circle in terms of radian and in degree.

Let Ø be the angle subtended by circle.

______________________________

We know that

Ø = $\dfrac{l}{r}$

Put the known values in above equation

=> Ø = $\dfrac{10}{50}$

=> Ø = $\dfrac{1}{5}$

_______________________________

In radians...

Ø = $\dfrac{1}{5}$ radians

___________ $\bold{[ANSWER]}$

_______________________________

Now..

Ø = $\bigg(\dfrac{1}{5} \: \times \: \dfrac{360}{\pi} \bigg)$ °

Ø = $\bigg(\dfrac{72}{\pi} \bigg)$ °

______________________________

In degree ...

Ø = $\bigg(\dfrac{72}{\pi} \bigg)$ °

________ $\bold{[ANSWER]}$

______________________________