Calculate, correct to three significant figures, the leng...
Calculate, correct to three significant figures, the length of the arc AB in the diagram above.
[Take π=22/7]
32.4 cm
30.6 cm
28.8 cm
30.5 cm
Correct answer is B
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 = \frac{θ}{360^o} \times 2\pi r
⇒ L = \frac {134.76}{360} \times 2 \times \frac {22}{7} \times 13 = \frac {77082.72}{2520}
∴ L = 30.6cm (to 3 s.f)
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