the angle of elevation of a pillar from a point A on the ground is 45° and from a point B diametrically opposite to A and on the other side of the pillar is 60°. Find the height of the pillar given that the distance between A and B is 15 m.
Answers
Given : the angle of elevation of a pillar from a point A on the ground is 45° and from a point B diametrically opposite to A and on the other side of the pillar is 60° . distance between A and B is 15 m.
To find : height of the pillar
Solution:
Let say height of pillar = h m
Tan 45° = Height of pillar / Distance of A from pillar bottom
=> 1 = h/Distance of A from pillar bottom
=> Distance of A from pillar bottom = h m
Distance of A from pillar Bottom + Distance of B from pillar bottom = 15 m
=> h + Distance of B from pillar bottom = 15 m
=> Distance of B from pillar bottom = 15-h m
Tan 60° = Height of pillar / Distance of B from pillar bottom
=> √3 = h / (15 - h)
=> 15√3 - h√3 = h
=> 15√3 = h(√3 + 1)
=> h = 15√3/(√3 + 1)
=> h ≈ 9.5 m
Height of pillar≈ 9.5 m or 15√3/(√3 + 1) m
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Answer:
xm = 9.51m
I have taken x m as height of the pillar
{m means metre}
