The great galaxy in Andromeda has an angular diameter along its long axis of about 5 degree. Its distance is about 2.2 million light years. What is its linear diameter?
I answered this question about three days ago. All you had to do was multiply two numbers, which I provided. Please read it again and perform the remaining step.
http://www.jiskha.com/display.cgi?id=1269724510
It was 2*pie*2.2(5/360)=.1919*10=1.92 rounded
To find the linear diameter of the great galaxy in Andromeda given its angular diameter and distance, we can use basic trigonometry.
1. Start by converting the angular diameter from degrees to radians. Since 1 degree is equal to π/180 radians, we can calculate the angular diameter in radians by multiplying it by π/180:
Angular diameter in radians = 5 degrees * (π/180) ≈ 0.087 radians
2. Use the small-angle approximation, which approximates the arc length across a small angle in a circle as the radius multiplied by the angle. In this case, the arc length is equal to the linear diameter of the galaxy, and the radius is equal to the distance to the galaxy.
Linear diameter ≈ Distance * Angular diameter in radians
Linear diameter ≈ 2.2 million light years * 0.087 radians
3. Convert the linear diameter from light years to another unit if needed. For example, if you want the linear diameter in kilometers, you could convert the light years using the conversion factor of 1 light year ≈ 9.461 × 10^12 km.
Linear diameter ≈ 2.2 million * 9.461 × 10^12 km * 0.087 radians
Performing the calculation should give you the linear diameter of the great galaxy in Andromeda.