The sun subtends an angle if about 0.5° to us on earth,150 million km away. estimate the radius of the sun.

We can use the figure attached as a guide to estimate the radius of the Sun.

How?

Well, if we consider the angle ,  this is the angle subtended.

By definition "the angle subtended (in radians) is given by an arc whose length is equal to the radius ":

  (1)

In this case the red arc in the figure is the arc length , the distance between the Earth and the Sun and we need to convert the to radians, as follows:

If:   (2)

Then:   (3)

Now we can substitute (3) in (1):

   (4)

and find the arc length :

   (5)

Approximating this arc length to the diameter of the Sun, we can say that

But, we are asked to estimate the radius of the Sun, and we can find it knowing the radius is one half of the diameter:

   (6)

Finally we get the estimation of the radius of the Sun: