Question

An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

• A. $50^\circ$
• B. $60^\circ$
• C. $45^\circ$
• D. $30^\circ$

Hint:

Notice the decimal relationships during simplification to save time.
Since $17.6$ is exactly $8$ times $2.2$, the calculation simplifies directly to $\frac{360^\circ}{8} = 45^\circ$.

Answer 1

The Correct Option is C

Step 1: Recall the arc length formula in radians form, which avoids fractions with $360^\circ$.
\[ l = r\theta \quad (\theta \text{ in radians}) \]
Step 2: Solve for $\theta$ in radians.
\[ \theta = \frac{l}{r} = \frac{2.2}{2.8} = \frac{11}{14} \text{ radians} \]
Step 3: Convert radians to degrees using $180^\circ = \pi$ radians, with $\pi = \frac{22}{7}$.
\[ \theta = \frac{11}{14} \times \frac{180}{\pi} = \frac{11}{14} \times \frac{180 \times 7}{22} \]
\[ \theta = \frac{11 \times 180 \times 7}{14 \times 22} = 45^\circ \]
Step 4: Conclude.
This matches option (3).
\[ \boxed{45^\circ} \]