Question

Find the degree measure of the angle subtended at the center of a circle of radius 100 cm by an arc of length 22 cm. (Useπ= 22/7 )////

Answer 1

$\bigstar \underline{\underline{\sf \bf Given:-}}$

• Radius=100cm
• Length = 22cm

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

• Degree measure of the angle subtented at the centre of the circle.

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

We know :

$\mapsto \boxed{\boxed{\sf l=r \ \theta}}$

Where,

=> l= length

=> r = radius

=>θ=angle subtended

Now,

$:\implies \sf l=r\ \theta \\\\:\implies \sf \theta =\frac{l}{r} \\\\:\implies \bold{ \theta=\frac{22}{100} radians.}$

We should now convert radians to degrees ,

$\mapsto \boxed{\boxed{\sf Radian\ measure=\frac{\pi}{180}\times degree\ measure }}$

$:\implies \sf \frac{22}{100} =\frac{\pi}{180} \times degree\ measure \\\\(\pi = 22/7)\\\\:\implies \sf Degree\ measure = \frac{22}{100} \times \frac{180}{22} \times 7\\\\:\implies \sf Degree\ measure=\frac{126}{10} \\\\\\:\implies \sf 12^o +\frac{6^o}{10} \\\\\bold{(1^o=60')}\\\\:\implies 12^o +( \frac{6\times 60}{10})'\\\\:\implies 12^o +(\frac{360}{10} )'\\\\:\implies \sf 12^o + 36'\\\\:\implies \boxed{\boxed{\bold {\sf \theta= 12^o 36'.}}}$

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HOPE IT HELPS !

Answer 2

$\bigstar \underline{\underline{\sf \bf Given:-}}$

Radius=100cm

Length = 22cm

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

Degree measure of the angle subtented at the centre of the circle.

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

We know :

$\mapsto \boxed{\boxed{\sf l=r \ \theta}}$

Where,

=> l= length

=> r = radius

=>θ=angle subtended

Now,

$:\implies \sf l=r\ \theta \\\\:\implies \sf \theta =\frac{l}{r} \\\\:\implies \bold{ \theta=\frac{22}{100} radians.}$

We should now convert radians to degrees ,

$\mapsto \boxed{\boxed{\sf Radian\ measure=\frac{\pi}{180}\times degree\ measure }}$

$:\implies \sf \frac{22}{100} =\frac{\pi}{180} \times degree\ measure \\\\(\pi = 22/7)\\\\:\implies \sf Degree\ measure = \frac{22}{100} \times \frac{180}{22} \times 7\\\\:\implies \sf Degree\ measure=\frac{126}{10} \\\\\\:\implies \sf 12^o +\frac{6^o}{10} \\\\\bold{(1^o=60')}\\\\:\implies 12^o +( \frac{6\times 60}{10})'\\\\:\implies 12^o +(\frac{360}{10} )'\\\\:\implies \sf 12^o + 36'\\\\:\implies \boxed{\boxed{\bold {\sf \theta= 12^o 36'.}}}$

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HOPE IT HELPS !