Solving a simple math and science problem. Could you please help out?

Question

Please how do I solve this? Or what is the answer?

Determine the angular size of the Orion Nebula. Give your answer in degrees?

∝=?

d=1500 light years

D=30 light years

Small angle formula:

D= (∝d)

_____

206,265

The above IS a fraction.

Thanks.

Answer 1

You just need to figure out the formula by the one you already have.

If D = (∝d)/(206 265) then you "pass" the denominator or dividing number to the other side of the equal sign, and this will do the opposite, in this case multiply, so you have

D*(206 265)=∝d

Now, you do the same so yo have the incognit alone, in one side of the equal sign, so the d its multiplying, it means in the other side will be dividing, and you have

(D*(206265)) / d = ∝

Change the letters for their value and calculate

Answer 2

Lets clean this up.  Your least-known data is to two places, so   D/ 2.1x10^5 = (alpha) d.  This gives you an answer of about 1x10^-7.  Now  this would be the angular size of the Nebula as it appears on earth compared to a 360 degree sweep.  Expressed in degrees, minutes and seconds, we would have 1 second of arc = 1/[360x60x60]= 1/(360*3600)= 1/1296000.  This is about 1/8th of that, so the size is about 1/8 second.