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 cm
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 cm
1). 15° 12’ 45”
2). 15° 11’ 45”
3). 10° 12’ 45”
4). 15° 12’ 40”
1 answers
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”.Other Questions
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