step 1
In the right triangle of the angle of 59 degrees and 30 minutes
59 degrees 30'=59.5 degrees
tan(59.5)=h/x
h=x*tan(59.5) -------> equation A
step 2
25 degrees 4'=25+4/60=25 1/15 degrees
tan(25 1/15)=h/(142+x)
h=(142+x)*tan(25 1/15) -------> equation B
Equate equation A and equation B
x*tan(59.5)=(142+x)*tan(25 1/15)
x*tan(59.5)=142*tan(25 1/15)+x*tan(25 1/15)
solve for x
x*tan(59.5)-x*tan(25 1/15)=142*tan(25 1/15)
x[tan(59.5)-tan(25 1/15)]=[142*tan(25 1/15)]
x=[142*tan(25 1/15)]/[tan(59.5)-tan(25 1/15)]
x=54
Find the value of h
h=(54)*tan(59.5)
h=91.67 m
h=92 meters