Answer: 654498.469 km
We can use the figure attached as a guide to estimate the radius of the Sun.
How?
Well, if we consider the angle [tex]aeb=\theta=0.5\º[/tex], this is the angle subtended.
By definition "the angle subtended (in radians) [tex]\theta[/tex] is given by an arc whose length [tex]l[/tex] is equal to the radius [tex]d[/tex]":
[tex]\theta=\frac{l}{d}[/tex] (1)
In this case the red arc in the figure is the arc length [tex]l[/tex], [tex]d[/tex] the distance between the Earth and the Sun and we need to convert the [tex]0.5\º[/tex] to radians, as follows:
If: [tex]360\º=2\pi rad[/tex] (2)
Then: [tex]0.5\º\frac{2\pi rad}{360\º}=0.0087rad[/tex] (3)
Now we can substitute (3) in (1):
[tex]0.0087rad=\frac{l}{150000000km}[/tex] (4)
and find the arc length [tex]l[/tex]:
[tex]l=1308996.93km[/tex] (5)
Approximating this arc length to the diameter [tex]D[/tex] of the Sun, we can say that [tex]D=1308996.93km[/tex]
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:
[tex]r=\frac{D}{2}[/tex] (6)
[tex]r=\frac{1308996.93km}{2}[/tex]
Finally we get the estimation of the radius of the Sun:
[tex]r=654498.469km[/tex]
