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3.Trigonometrical Ratios, Functions and Identities
easy
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 $\pi=\frac{22}{7}$ ).
A
$12^{\circ} 36^{\prime}$
B
$12^{\circ} 36^{\prime}$
C
$12^{\circ} 36^{\prime}$
D
$12^{\circ} 36^{\prime}$
Solution
We know that in a circle of radius $r$ unit, if an are of length $l$ unit subtends an angle $\theta$ radian at the centre, then
$\theta=\frac{1}{r}$
Therefore, for $r=100 \,cm , l=22 \,cm ,$ we have
$\theta=\frac{22}{100}$ radian
$=\frac{180}{\pi} \times \frac{22}{100}$ degree
$=\frac{180 \times 7 \times 22}{22 \times 100}$ degree
$=\frac{126}{10}$ degree
$=12 \frac{3}{5}$ degree
$=12^{\circ} 36^{\prime} \quad \quad\left[1^{\circ}=60^{\prime}\right]$
Thus, the required angle is $12^{\circ} 36^{\prime}$
Standard 11
Mathematics
