Question

Find the degree measures of the angle subtended at the centre of a circle of radius 100cm by an arc of length 22cm (use π=227)

Answer 1

θ=lrθ=lrθθ=angle subtended by arcll=length of the arcrr=radius of the circle1 radian=(180π)(180π)Given :l=22l=22cm,r=100cmθ=lrθ=lr⇒22100⇒22100θ=0.22θ=0.22radiansWe know that1 radian=(180π)(180π)0.22 radian=0.22×180∘π0.22×180∘π⇒0.22×180∘22/7⇒0.22×180∘22/7⇒0.22×180×722⇒0.22×180×722⇒12610⇒12610=12∘36′=12∘36′Thus the degree measures of the angle subtended at the centre of the circle is 12∘36′12∘36′Hence (B) is the correct answer.

Answer 2

Step-by-step explanation:

$\bullet\:\:\textsf{Radius = (r) = \textbf{100 cm}}$

$\bullet\:\:\textsf{Arc Length = (l) = \textbf{22 cm}}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\qquad \tiny \dag \: \underline {\bf Formula \: used :}$

$\bigstar \: \: \sf l = r \: \theta \: \: \bigstar$

$\qquad \tiny \dag \: \underline {\bf Putting \: the \: value :}$

$: \implies \sf 22 = 100 \times \theta$

$: \implies \underline{ \boxed{\sf \theta = \dfrac{22}{100} \: radians}}$

____________________

$\qquad \tiny \dag \: \purple{\underline {\bf We \: need \: to \: find \: \theta \: into \: degree:}}$

$\dashrightarrow\:\:\sf Radian \: measure = \dfrac{\pi}{180} \times Degree \: measure \\ \\ </p><p>$

$\dashrightarrow\:\:\sf \dfrac{22}{100} = \dfrac{22}{180} \times \dfrac{1}{7} \times Degree \: measure \\ \\ </p><p>$

$\dashrightarrow\:\:\sf \dfrac{22}{100} \times \dfrac{180}{22} \times \dfrac{7}{1} = Degree \: measure$

$\dashrightarrow\:\: \sf Degree \: measure = \frac{126}{10}$

$\dashrightarrow\:\: \sf Degree \: measure = 12.6^{\circ}$

$\dashrightarrow\:\: \sf Degree \: measure = 12^{ \circ} + 6^{\circ}$

$\dashrightarrow\:\: \sf Degree \: measure = 12^{\circ} + (0.6 \times 60)$

$\dashrightarrow\:\: \underline{ \boxed{ \sf Degree \: measure = 12^{\circ} \: 36'}}$