Calculate, correct to three significant figures, the length of the arc AB in the diagram above. [Take π=22∕7]
Consider ∆XOB and using Pythagoras theorem
132 = 122 + h2
⇒ 169 = 144 + h2
⇒ 169 - 144 =h2
⇒ 25 = h2
⇒ h = √25 = 5cm
tan θ = oppadj
⇒ tan θ = 125 = 2.4
⇒ θ = tan−1(2.4)
⇒ θ = 67.380
∠AOB = 2θ = 2 x 67.38o = 134.76o
L = θ360o×2πr
⇒ L = 134.76360×2×227×13=77082.722520
∴ L = 30.6cm (to 3 s.f)
