From top of a small hill,the base of a vertical cliff has an angle of depression 30° and the top of the cliff has an angle of elevation of 45°.if the height of the cliff is 273.2m find the height of the hill
Answers
Given : From top of a small hill,the base of a vertical cliff has an angle of depression 30° and the top of the cliff has an angle of elevation of 45° . height of the cliff is 273.2m
To find : the height of the hill
Solution:
Let say height of hill = h m
Then height of cliff above hill = 273.2 - h m
top of the cliff has an angle of elevation of 45° from top pf hill
=> tan 45° = (273.2 - h)/horizontal Distance between hill & cliff
=> 1 = (273.2 - h)/horizontal Distance between hill & cliff
=> horizontal Distance between hill & cliff = 273.2 - h m
From top of a small hill,the base of a vertical cliff has an angle of depression 30
=> Tan 30° = height of hill / horizontal Distance between hill & cliff
=> 1/√3 = h/(273.2 - h)
=> 273.2 - h = √3 h
=> 273.2 = h(√3 + 1)
=>273.2 = h(1.732+ 1)
=> 273.2 = h(2.732)
=> h = 100
the height of the hill = 100 m
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