An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree,...
MATHEMATICS
WAEC 2008
An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [π = \(\frac{22}{7}\)]
- A. 11o
- B. 20o
- C. 22o
- D. 75o
Correct Answer: D. 75o
Explanation
Length of an arc = \(\frac{\theta}{360} \times 2\pi r\)
18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\)
\(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\)
= 75o (approx.)
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