Why is the parallax method not used to measure the distance of stars that are $100$ light-years away?

Calculate the angle of $(a)$ $1^{\circ}$ (degree),$(b)$ $1^{\prime}$ (minute of arc),and $(c)$ $1^{\prime \prime}$ (second of arc) in radians. Use $360^{\circ} = 2\pi \text{ rad}$,$1^{\circ} = 60^{\prime}$,and $1^{\prime} = 60^{\prime \prime}$.

The angle of $1^{\prime}$ (minute of arc) in radian is nearly equal to

Which of the following pairs is incorrect?

$(a)$ The earth-moon distance is about $60$ earth radii. What will be the angular diameter of the earth (approximately in degrees) as seen from the moon?
$(b)$ The moon is seen to have an angular diameter of $(1/2)^{\circ}$ from the earth. What is its relative size compared to the earth?
$(c)$ From parallax measurement,the sun is found to be at a distance of about $400$ times the earth-moon distance. Estimate the ratio of sun-earth diameters.

Which of the following is the most precise device for measuring length?