Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of the flag pole at an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flag pole increased to 450. What is the height of the flag pole? (3m)
Answers
Given : Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of the flag pole at an angle of elevation 30° . When he moved 10 m towards the flag post the angle of elevation of the top of the flag pole increased to 45°
To find : What is the height of the flag pole
Solution:
Let say height of flag pole = H m
Horizontal Distance of Boy from bottom of Flag = d m
Height of Flag above Boy height = H - 1.5 m
Tan 30° = ( H - 1.5)/d
=> 1/√3 = ( H - 1.5)/d
=> d = H√3 - 1.5√3
he moved 10 m towards the flag post
=> Horizontal Distance of Boy from bottom of Flag = d - 10 m
Tan 45° = ( H - 1.5)/(d - 10)
=> 1 = ( H - 1.5)/(d - 10)
=> d - 10 = H - 1.5
=> d = H + 8.5
H√3 - 1.5√3 = H + 8.5
=> H (√3 - 1) = 8.5 + 1.5√3
=> H = (8.5 + 1.5√3)/ (√3 - 1)
=> H = 15.16 m
height of the flag pole = 15.16 m
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