Question

What is the angle of an arc of circular length 15.7 cm subtends at centre? The radius of circular arc is 30 cm.

Answer 1

Answer:

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Answer 2

SOLUTION

TO DETERMINE

The angle of an arc of circular length 15.7 cm subtends at centre when radius of circular arc is 30 cm.

EVALUATION

Here by the given condition

S = Length of the arc = 15.7 cm

r = Radius of circular arc = 30 cm

Let θ = Required angle in radians

We know that

S = rθ

Thus we get

$\displaystyle \sf{ \implies \: \theta = \frac{15.7}{30} \: \: \: radians}$

$\displaystyle \sf{ \implies \: \theta = { \bigg( \frac{15.7}{30} \times \frac{180}{ \pi} \bigg)}^{ \circ} }$

$\displaystyle \sf{ \implies \: \theta = { \bigg( \frac{15.7}{30} \times \frac{180}{ 3.14} \bigg)}^{ \circ} }$

$\displaystyle \sf{ \implies \: \theta = { \bigg( \frac{1570}{30} \times \frac{180}{ 314} \bigg)}^{ \circ} }$

$\displaystyle \sf{ \implies \: \theta = { \bigg( 5 \times 6 \bigg)}^{ \circ} }$

$\displaystyle \sf{ \implies \: \theta = { 30}^{ \circ} }$

FINAL ANSWER

The required angle = 30°

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