Problem Solving

Question attached

Draw a vertical perpendicular from points P and Q to x-axis and name those points as R and S.

Angle PRO = 90 degrees
Length OR = root(3)
Length PR = 1
Now, we can say that triangle PRO is a 30-60-90 triangle keeping in mind 1:root(3):2 ratio for this type of triangle.
Angle OPR = 60 degrees and Angle POR = 30 degrees
Therefore, Length OP = 2

Now, we know that Angle POQ = 90 degrees [From the diagram]. We also know that Angle POR = 30 degrees.
Therefore, Angle QOS = 180 - (90+30) = 60 degrees
We already have a perpendicular from Point Q to x-axis. So, Angle QSO = 90 degrees.
Therefore, Angle OQS = 180 - (90+60) = 30 degrees

So we have found that Angle OQS = 30, Angle QOS = 60 and Angle QSO = 90

Therefore, Length OS = 1 [Since Angle OQS = 30 degrees]
Length QS = root(3) [Since Angle QOS = 60 degrees]
Length OQ = 2 [Since Angle QSO = 90 degrees]

So, Point (s,t) is [1,root(3)]. Therefore, s is 1.

Let me know if you have any doubts