A particular bird’s eye can just distinguish objects that subtend an angle no smaller than about 4.0×10^-4 rads.

(a) How many degrees is this?

(b) How small an object can the bird just distinguish when flying at a height of 160 m

Please show work, thank you.

Answer:Part a)

Angle in degree is given as

[tex]\theta = 0.023 ^o[/tex]

Part b)

Size of the object is

[tex]Length = 0.064 m[/tex]

Explanation:Part a)

As we know that

180 degree = [tex]\pi[/tex] radian

so we have

[tex]\theta = 4.0 \times 10^{-4} rad[/tex]

so we have

[tex]\theta = 4.0 \times 10^{-4} \times \frac{180}{\pi}[/tex]

[tex]\theta = 0.023 ^o[/tex]

Part b)

As we know that the relation of angle with radius is

[tex]\theta = \frac{arc}{radius}[/tex]

[tex]4 \times 10^{-4} = \frac{Length}{160}[/tex]

[tex]Length = 0.064 m[/tex]