We have PQ as a vertical tower
In ΔYZQ tan 45∘=QZYZ
QZYZ=1
QZ=YZ ...(i)
And, in ΔXPQ
tan 60∘=QPXP
√3=QZ+40XP
√3=QZ+40YZ (∵ XP=YZ)
√3 QZ=QZ+40 [Using (i)]
√3 QZ−QZ=40
QZ (√3−1)=40
QZ=40√3−1=40√3−1×√3+1√3+1
= 20 (√3+1)
= 20 (2.73)
= 54.60 m
∴ QZ=54.6 m
And PQ=XY+QZ=(54.6+40) m=94.6 m.