The Sun’s angular diameter is measured to be 1920’’. The distance of the sun from the earth is $1.496\times {10}^{11}m$. What is the diameter of the sun? 

The specified angular diameter is a measurement of the angle between the sun's poles taken from a certain location on earth. Provided that the diameter of the sun is equal to its diameter divided by the separation between it and the earth, we have given an angular diameter. The sun's diameter is equal to the arc length of a circle whose radius is equal to the distance between it and the earth, and whose angle is equal to the earth's angular diameter.

$\theta ={1920}^{\text{'}\text{'}}=$$\frac{1920°}{60\times 60}$
$=\frac{1920}{60\times 60}\times \frac{\pi }{180}\mathrm{rad}=0.0093\text{ radians }$
$D=L\theta$
Diameter of Sun, $D=\left(1.496\times {10}^{11}\times 0.0093\right)\mathrm{m}$
$=1.39\times {10}^9 \mathrm{m}$

Hence, the correct answer is option B.