Question

A person observes that the full length of a train subtends an angle of $15^\circ$. If the distance between the train and the person is $3$ km, the length of the train, calculated using parallax method, in meters is

• A. $45$
• B. $45\pi$
• C. $250\pi$
• D. $250$
• E. $450$

Hint:

For small angles, always use radians in formulas like $L = D\theta$. Unit consistency is very important.

Answer 1

The Correct Option is C

Concept:
In the parallax method, when an object subtends a small angle $\theta$ at a distance $D$, its length is given by: \[ L = D\theta \quad (\theta \text{ in radians}) \]

Step 1: Convert angle into radians.
\[ \theta = 15^\circ = \frac{15\pi}{180} = \frac{\pi}{12} \]

Step 2: Convert distance into meters.
\[ D = 3 \text{ km} = 3000 \text{ m} \]

Step 3: Apply formula.
\[ L = 3000 \times \frac{\pi}{12} = 250\pi \]