The angle subtended by a coin of radius 1 cm held at a distance of 80 cm from your eyes is

The correct option is 1.43°.

To find the angle subtended by the coin at the eye, we can use the relation between arc length, radius, and the subtended angle. Since the distance of the coin from the eye is much larger than the size of the coin, we can use the small-angle approximation.

Given data:
Radius of the coin, $r=1\mathrm{cm}$
Diameter of the coin, $d=2r=2\times 1\mathrm{cm}=2\mathrm{cm}$
Distance of the coin from the eye, $D=80\mathrm{cm}$

The angle $\theta$ in radians subtended by the diameter of the coin is given by the formula:
$\theta \approx \frac{\text{Diameter of the coin}}{\text{Distance from the eye}}=\frac{d}{D}$

Substituting the given values:
$\theta \approx \frac{2}{80}\text{rad}=0.025\text{rad}$

To convert the angle from radians to degrees, we multiply by $\frac{180}{\pi }$:
$\theta \approx 0.025\times \frac{180}{\pi }°$

Using the value of $\pi \approx 3.1416$:
$\theta \approx 0.025\times 57.2958°\approx 1.432°$

Therefore, the angle subtended by the coin is approximately 1.43°.