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Diameter of a planet, known the angular size and distance

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data
    a planet is 5x10^8 km from its sun, from the planet, the sun has an angular size of 1 degree. what is the diameter of the sun?


    2. Relevant equations



    3. The attempt at a solution
    ive drawn a diagram with the sun and the planet, with the distance between written in and the 1 degree size of the sun on the planets surface. i was thinking of using trignometry, since i know one angle and the length going through the center of the imaginary triangle, but im not sure, i havent used trig in a while
     
  2. jcsd
  3. Sep 26, 2009 #2
    alright so heres what i worked out. since from the planet the angular distance is 1 degree and the distance to the sun to the sun is 3x10^5, i draw a triangle with one degree at the planet and the wider part of the triangle is defined by the base of the triangle. i cut the triangle down the center (cutting the 1 degree in half) making 2 right angle triangles, since one angle is 90 and i cut the 1 degree in half, thats 0.5 degrees and the third is 89.5. one side of the triangle is 300000 km. heres my work using trig:
    sin(89.5)= 300000/x (x being the hypotenuse)
    x= 300011

    now i use Pythagorus to get the length of the base of the right triangle, which is the radius of the sun.
    300000^2+b^2= 30011^2
    b= 2569

    since the radius is needed, i multply this by 2 to get a diameter of 5138 km.


    is this right, the only thing im uncertain of in my solution is the i cut the one triangle to make 2. can i cut it down the middle like that making two triangles with 0.5 degrees from one triangle with 1 degree?
     
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