When Venus is 45,000,000 kilometers from Earth, it has an angular size of 55 arc seconds. From this, what is the diameter of Venus, in kilometers?

11999.14 km

Explanation:

Given that the angular size of the Venus with radius, 45,000,000 kilometers is 55 arc seconds.

Also,

1 arc seconds = 1 / 3600 degrees

1 degree = π / 180 radians

So,

1 arc seconds = π / (3600 * π) radians

So,

55 arc seconds = 55 * π / (3600 * 180) radians

Also,

Arc length is:

s = r * theta

s = 45000000 * (55 * π / (3600 * 180))

s = 11999.14 km