Math, asked by kotipallisrikedddddd, 4 months ago

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. (Useπ= 22/7 )

Answers

Answered by αηυяαg
67

 \huge{\bf{\underline{\green{Given:}}}}

  • Radius of Circle = 100 cm

  • Length of Arc = 22 cm

 \huge{\bf{\underline{\green{To\:Find:}}}}

  • Degree measure of the angle subtended at the centre of a circle.

 \huge{\bf{\underline{\green{Formula\:Used:}}}}

  • {\bf{\boxed{r=\dfrac{l}{θ}}}}

 \huge{\bf{\underline{\green{Solution:}}}}

Using Formula,

\sf :\implies\:r=\dfrac{l}{θ}

Putting Values,

\sf :\implies\:100=\dfrac{22}{θ}

\sf :\implies\:θ=\dfrac{22}{100}

\sf :\implies\:θ=\dfrac{11}{50}\: radians

Now,

\sf :\implies\:θ=(\dfrac{11}{50}\times \dfrac{180}{\pi})°

\sf :\implies\:θ=(\dfrac{11}{5}\times \dfrac{18\times 7}{22})°

\sf :\implies\:θ=(\dfrac{11}{5}\times \dfrac{9\times 7}{11})°

\sf :\implies\:θ=(\dfrac{693}{55})°

\sf :\implies\:θ=(12\dfrac{33}{55})°

\sf :\implies\:θ=12°(\dfrac{3}{5}\times 60)'

\sf :\implies\:θ=12°36'

Hence, The Degree measure of the angle subtended at the centre of a circle is 12°36'.

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