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 \(\pi = ^{22}/_7\)]
32.4 cm
30.6 cm
28.8 cm
30.5 cm
Correct answer is B
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)
Similar Questions
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13 ...
Evaluate \(log_{10}5 + log_{10}20\)...
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\) ...
Simplify \(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)...
If P \(=\left[\begin{array}{cc}x+3 & x+2\\ x+1 & x-1\end{array}\right]\) evaluate x if |P| ...