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: Use the radian relation instead of the degree formula.
In radians, arc length $l = r\theta$, so $\theta(\text{in radians}) = \frac{l}{r} = \frac{2.2}{2.8} = \frac{11}{14}$.
Step 2: Convert radians to degrees using pi = 22/7. \[ \theta = \frac{11}{14} \times \frac{180}{\pi} = \frac{11}{14} \times 180 \times \frac{7}{22} \]
Step 3: Simplify the product. \[ \theta = \frac{11 \times 180 \times 7}{14 \times 22} = \frac{13860}{308} = 45^\circ \]
\[ \boxed{\theta = 45^\circ} \]