In the right triangle #triangle QYX#, the cotangent function for #/_Q=34^@# is
#color(white)("XXX")cot(34^@)= (abs(QY))/(abs(YX)) = (abs(QY))/(200 "m")#
#color(white)("XXX")abs(QY) = 200 "m" xx cos(34^@)#
#color(white)("XXX")cot(34^@) = 1.482561# (using calculator)
#color(white)("XXX")abs(QY) = 200 xx 1.482561 "m"#
#color(white)("XXXXX") = 297 "m"# (to nearest meter)
#color(black)("---------------------------------------------------------------")#
Similarly in #triangle PYX#
#color(white)("XXX")abs(PY) = 180 "m"# (to the nearest meter)
#color(black)("---------------------------------------------------------------")#
The Law of Cosines
#color(white)("XXX")c^2 = a^2+b^2-2ab*cos(/_C)#
Using the previously determined values of #abs(QY)# as #a# and #abs(PY)# as #b# plus the given angle #/_PYQ = 84^@# as #/_C#
#color(white)("XXX")c^2 = 297^2+180^2-2*297*180*cos(84^@)#
#color(white)("XXX")=109186#
#color(white)("XXX")abs(PQ) = c = sqrt(109186) = 330 "m"#
