Let height of pole be \( h \), distance from X be \( x \), and distance from Y be \( y \).
From X:
\[
\tan 30^\circ = \frac{h}{x} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow h = \frac{x}{\sqrt{3}}
\]
From Y:
\[
\tan 60^\circ = \frac{h}{y} \Rightarrow \sqrt{3} = \frac{h}{y} \Rightarrow h = y\sqrt{3}
\]
Equating:
\[
\frac{x}{\sqrt{3}} = y\sqrt{3} \Rightarrow x = 3y
\]
Now,
\[
x + y = 135 \Rightarrow 3y + y = 135 \Rightarrow 4y = 135 \Rightarrow y = 33.75
\text{So distance from Y = } y = 67.5
\]