From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be 45∘ and 30∘ respectively. Find the height of the hill.
Here, AB is the hill and P and Q are two consecutive kilometer stones.
Let the height of the hill AB be h m and BP = x m.
PQ = 1 km = 1000 m
BQ=BP+PQ=x+1000tan 30o=ABBQ1√3=hx+1000x+1000=√3h√3h=h+1000 [Using (1)](√3−1)h=1000h=1000(√3−1)h=1000(√3+1)(√3−1)(√3+1)h=1000(√3+1)(3−1)h=1000(√3+1)2h=500(√3+1)h=500(1.73+1)h=500×2.73=1365 m
Thus, the height of the hill is 1365 m