Question

Find the degree measure of angle substended at the centre of a circle of an radius 100cm by an arc of length 22.​

Answer 1

Answer:

• The required degree measure is 12°36'.

Step-by-step explanation:

We have been given that angle subtended at the centre of a circle of an radius 100cm by an arc of length 22.

• Length of arc = 22 cm
• Radius of circle = 100 cm.

We have to find angle subtended at the centre of a circle.

We have a formula, θ =l/r

→ θ =l/r

→ θ = 22/100

∴ θ = 22/100 radian

Step: Convert radian into degree.

→ Radian = π/180 × degree measure

→ π × Degree measure = 180 × Radian

→ 22/7 × Degree measure = 180 × 22/100

→ Degree measure = (180 × 22/100 × 7)/22

→ Degree measure = 126/100°

Step: Convert into two forms i.e degree and minute.

→ Degree measure = 126/100°

= 12° + 6°/10

= 12° + [ (6 × 60/10)']

= 12° + 36'

= 12°36'

Therefore,The required degree measure is 12°36'.

Answer 2

Step-by-step explanation:

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

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

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

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

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

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

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

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

____________________

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

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

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

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

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

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

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

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

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