Question

What is the angular diameter (in arcseconds) of an object that has a linear diameter of 75 cm and a distance of 2 km?

Answer 1

The angular diameter is 77.35 arc-seconds.

Step-by-step explanation:

The angular diameter, as shown in the figure, is the angle
`x` subtended by the the diameter of the object.

Before we do the calculation, we first convert everything to meters.

The diameter of the of the object in meters is

75cm =0.75m,

and the distance to the object in meters is

2 km = 2000 m.

Now, from trigonometry we get:

`tan ((x)/(2) )= (radius)/(length) = (0.75/2)/(2000) \\\\(x)/(2) = tan^(-1)((0.75/2)/(2000))\\\\(x)/(2)= 0.0107\\\\\boxed{x= 0.0215^o}`

and since 1 degree = 3600 arc-seconds,
`x` in arc-seconds is

`x= 0.0215*3600 \\\\\boxed{x= 77.35''}`