Question
From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be 30° and 45° respectively. Find the height of the hill.
Solution
Let CD be the hill of height h km. Let A and B be two stones due east of the hill at a distance of 1 km. from each other. It is also given that the angles of depression of. stones A and B from the top of a hill be 30° and 45° respectively.
Let BC = x km
In right triangle BCD, we have
In right triangle ACD, we have
Comparing (i) and (ii), we get
Hence, the height of hill is 1.365.
