Q11. Two pillars of equal height stand on either side of a roadway 150

1.	Q11. Two pillars of equal height stand on either side of a roadway 150m wide.From a point on the roadway between the pillar, the angles of elevation of the topof the pillars are 60Â°and 30Â°. Find the height of pillars and the position of thepoint.
Answer» Let the height of the equal pillars be AB = CD = h Given, width of the road is 150 m Let BE = x, the DE = 150 - x In right angle triangle ABE, tan 60 = h/x => √3 = h/x => h = √3x ............1 In right angle triangle CDE, tan 30 = h/(150 - x) => 1/√3 = h/(150 - x) => √3h = 150 - x => √3h = 150 - h/√3 {from equation 1} => √3h + h/√3 = 150 => (3h + h)/√3 = 150 => 4h = 150√3 => h = 150√3/4 => h = 37.5√3 m So, the height of the equal pillers is 37.5√3 m

Q11. Two pillars of equal height stand on either side of a roadway 150m wide.From a point on the roadway between the pillar, the angles of elevation of the topof the pillars are 60Â°and 30Â°. Find the height of pillars and the position of thepoint.

Answer»

Let the height of the equal pillars be AB = CD = h

Given, width of the road is 150 m

Let BE = x, the DE = 150 - x

In right angle triangle ABE,

tan 60 = h/x

=> √3 = h/x

=> h = √3x ............1

In right angle triangle CDE,

tan 30 = h/(150 - x)

=> 1/√3 = h/(150 - x)

=> √3h = 150 - x

=> √3h = 150 - h/√3 {from equation 1}

=> √3h + h/√3 = 150

=> (3h + h)/√3 = 150

=> 4h = 150√3

=> h = 150√3/4

=> h = 37.5√3 m

So, the height of the equal pillers is 37.5√3 m