Question

What is the angular width of a person's thumb viewed at arm's length? Assume that the width of the thumb is 17.3 mm and that the distance between the eyes and the thumb is 71.9 cm. Use the small-angle approximation and then convert the answer to degrees.

Answer 1

`\theta_(degrees) =0.024\°=0\°1'26.62''`

Step-by-step explanation:

To solve the problem it is necessary to take into account the concepts related to arc length and the radius that make up the measurements of an angle.

An angle is given by the length of arc displaced as a function of the radius, that is

`\theta = (Arc_(length))/(Radius)`

`\theta = (17.3*10^(-3))/(71.9*10^(-2))`

`\theta = 0.02406rad`

360° is equal to do
`2\pi` rad, therefore:

`\theta_(degrees) = 0.02406rad *((180\°)/(2\pi rad))`

`\theta_(degrees) =0.024\°=0\°1'26.62''`