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

Question:

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

Solution:

We have:

Now,

$\theta=1^{\prime}=\left(\frac{1}{60}\right)^{\circ}=\left(\frac{1}{60} \times \frac{\pi}{180}\right)$ radian

We know,

$\theta=\frac{\text { Arc }}{\text { Radius }}$

$\Rightarrow \frac{1}{60} \times \frac{\pi}{180}=\frac{\text { Arc }}{5280}$

$\Rightarrow$ Arc $=\frac{5280 \times 22}{60 \times 180 \times 7}=1.5365 \mathrm{~m}$