Let F be the foot and S be the summit of the mountain FOS. Then, ∠OFS = 45º and therefore ∠OSF = 45º. Consequently,
OF = OS = h km(say).
Let FP = 1000 m = 1 km be the slope so that
∠OFP = 30º. Draw PM ⊥OS and PL ⊥OF.
Join PS. It is given that ∠MPS = 60º.
In ∆FPL, We have
Now, h = OS = OF = OL + LF
In ∆PSM, we have
⇒ SM = PM. tan 60º …..(ii)
[Using equations (i) and (ii)]