2023
Mathematics
JAMB
Calculate, correct to three significant figures, the length of the arc AB in the diagram above.[Take π=22/7]
A.
32.4 cm
B.
30.6 cm
C.
28.8 cm
D.
30.5 cm
Correct Answer: 30.6 cm
Explanation
Consider ∆XOB and using Pythagoras theorem 132 = 122 + h2 ⇒ 169 = 144 + h2 ⇒ 169 - 144 =h2 ⇒ 25 = h2 ⇒ h = √25 = 5cm tan θ = opp/adj ⇒ tan θ = 12/5 = 2.4 ⇒ θ = tan-1(2.4) ⇒ θ = 67.38o ∠AOB = 2θ = 2 x 67.38o = 134.76o L = θ/360o×2πr ⇒ L = 134.76/360 × 2 × (22/7) × 13 =77082.72/2520 ∴ L = 30.6cm (to 3 s.f)
Consider ∆XOB and using Pythagoras theorem 132 = 122 + h2 ⇒ 169 = 144 + h2 ⇒ 169 - 144 =h2 ⇒ 25 = h2 ⇒ h = √25 = 5cm tan θ = opp/adj ⇒ tan θ = 12/5 = 2.4 ⇒ θ = tan-1(2.4) ⇒ θ = 67.38o ∠AOB = 2θ = 2 x 67.38o = 134.76o L = θ/360o×2πr ⇒ L = 134.76/360 × 2 × (22/7) × 13 =77082.72/2520 ∴ L = 30.6cm (to 3 s.f)THIS WEEK's
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