Find the degree measure of the angle subtende | vedclass

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(A) We know that in a circle of radius $r$,if an arc of length $l$ subtends an angle $	heta$ in radians at the centre,then $	heta = \frac{l}{r}$.Giv

Vedclass · Accepted Answer

$12^{\circ} 36^{\prime}$

Vedclass · Answer

(A) We know that in a circle of radius $r$,if an arc of length $l$ subtends an angle $	heta$ in radians at the centre,then $	heta = \frac{l}{r}$.Given $r = 100 \, cm$ and $l = 22 \, cm$,we have:$	heta = \frac{22}{100} \, 	ext{radians}$.To convert radians to degrees,we use the relation $1 \, 	ext{radian} = \frac{180^{\circ}}{\pi}$.$	heta = \frac{22}{100} 	imes \frac{180}{\pi} \, 	ext{degrees}$.Substituting $\pi = \frac{22}{7}$:$	heta = \frac{22}{100} 	imes 180 	imes \frac{7}{22} = \frac{180 	imes 7}{100} = \frac{1260}{100} = 12.6^{\circ}$.Converting $0.6^{\circ}$ to minutes:$0.6^{\circ} = 0.6 	imes 60^{\prime} = 36^{\prime}$.Thus,the required angle is $12^{\circ} 36^{\prime}$.

Find the degree measure of the angle subtended at the centre of a circle of radius $100 \, cm$ by an arc of length $22 \, cm$ (Use $\pi = \frac{22}{7}$).

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