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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]

A.

32.4 cm

B.

30.6 cm

C.

28.8 cm

D.

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 = tan1(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)