Calculate, correct to three significant figures, the length of the arc AB in the diagram...
MATHEMATICS
JAMB 2023
Calculate, correct to three significant figures, the length of the arc AB in the diagram below.
[Take \(\pi = ^{22}/_7\)]
- A. 32.4 cm
- B. 30.6 cm
- C. 28.8 cm
- D. 30.5 cm
Correct Answer: B. 30.6 cm
Explanation
Consider ∠XOB and using Pythagoras theorem
13\(^2\) = 12\(^2\) + h\(^2\)
⇒ 169 = 144 + h\(^2\)
⇒ 169 - 144 =h\(^2\)
⇒ 25 = h\(^2\)
⇒ h = \(\sqrt25\) = 5cm
tan θ = \(\frac {opp}{adj}\)
⇒ tan θ = \(\frac{12}{5}\) = 2.4
⇒ θ = tan\(^{-1}\)(2.4)
⇒ θ = 67.38\(^0\)
∠AOB = 2θ = 2 x 67.38\(^o\) = 134.76\(^o\)
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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