Question

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

 

Answer 1

We have:
Radius = 5280 m
Now,
\[\theta = 1' = \left( \frac{1}{60} \right)^\circ = \left( \frac{1}{60} \times \frac{\pi}{180} \right)\text{ radian }\]
We know:

\[\theta = \frac{\text{ Arc }}{\text{ Radius }}\]
\[ \Rightarrow \frac{1}{60} \times \frac{\pi}{180} = \frac{\text{  Arc }}{5280}\]
\[ \Rightarrow \text{ Arc }= \frac{5280 \times 22}{60 \times 180 \times 7} = 1 . 5365 m\]