Question

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm \((Use\,{\pi}=\frac{22}{7}).\)

Answer 1

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then

\(θ=\frac{1}{r}\)

Therefore, forr = 100 cm, l = 22 cm, we have

\(θ=\frac{22}{100}\,radian=\frac{180}{\pi}×\frac{22}{100}\,degree=\frac{180×7×22}{22×100}\,degree\)

\(=\frac{126}{10}\,radian=12\frac{3}{5}\,degree=12°36' ........[1°=60']\)

Thus, the required angle is 12°36“²