Question 1043922
Make this drawing described:
Horizontal segment BA, point S slightly to the right of A and above it.
Interior angle at B is 84 degrees; interior angle at A is 87 degrees. Segment BA is 50 miles.


Sum of interior angles of triangle BAS will give measure of interior angle at S is 9 degrees.



One of the questions means, find measure of AS.  This can be done using Law Of Sines.
{{{sine(9)/50=sine(84)/AS}}}
Solve this for the value of measure of AS.



Distance from S to LINE BA is a little more complicated.
Start by extending the segment from point A along line BA; draw perpendicular segment from S to line BA.  You want this distance.  Call this some variable, maybe, y.


You now have a smaller, RIGHT Triangle of sides AS (which you found now), height y, new angle at angle A being 93 degrees; and you want to solve for y.  Understand too, AS is hypotenuse, and is opposite a right angle.
-
{{{AS*sin(93)=y}}}   (although not the only way...)
{{{y=AS*sin(93)}}}
{{{highlight(y=50(sine(84)/sine(9))sine(93))}}}, which you can simplify and compute.