Question

find the angular size of a circular object with a 1 - inch diameter viewed from a distance of 2 yards. the angular size of the object is (square^{circ}). (do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Convert units

First, convert 2 yards to inches. Since 1 yard = 36 inches, then 2 yards = 2×36 = 72 inches.

Step2: Use the small - angle formula

The small - angle formula is $\theta=\frac{s}{d}\times\frac{180^{\circ}}{\pi}$, where $\theta$ is the angular size in degrees, $s$ is the size of the object, and $d$ is the distance from the observer to the object. Here, $s = 1$ inch and $d=72$ inches.
Substitute the values into the formula: $\theta=\frac{1}{72}\times\frac{180^{\circ}}{\pi}$.

Step3: Calculate the angular size

$\theta=\frac{180^{\circ}}{72\pi}=\frac{5^{\circ}}{2\pi}\approx 0.79577^{\circ}\approx0.80^{\circ}$

Answer:

$0.80^{\circ}$