1.

In a circle of radius 6 cm, an arc of certain length subtends 20° 17’ at the center. Find in sexagesimal unit the angle subtended by the same arc at the center of a circle of radius 8 cm1). 15° 12’ 45”2). 15° 11’ 45”3). 10° 12’ 45”4). 15° 12’ 40”

Answer»

Let an ARC of length be m cm subtends 20° 17’ at the center of a circle of radius 6 cm and α° at the center of a circle of radius 8 cm. 

Now, 20° 17’ = {20 (17/60)}° 

= (1217/60)°

= 1217π/(60 × 180) radian [since, 180° = π radian]

And α° = πα/180 radian

We KNOW, the formula, s = rθ then we GET,

When the circle of radius is 6 cm; m = 6 × [(1217π)/(60 × 180)] ………… (i) 

And when the circle of radius 8 cm; m = 8 × (πα)/180 …………… (II)

Therefore, from (i) and (ii) we get; 

8 × (πα)/180 = 6 × [(1217π)/(60 × 180)]

Or, α = [(6/8) × (1217/60)]° 

Or, α = (3/4) × 20° 17’ [since, (1217/60)° = 20° 17’]

Or, α = 3 × 5°4’ 15” 

Or, α = 15° 12’ 45”.


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