Question

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.

Answer 1

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 2

Answer:

xm = 9.51m

I have taken x m as height of the pillar

{m means metre}