cloud above the lĂĽkeQl1. Two pillars of equal height stand on eithe

1.	cloud above the lĂĽkeQl1. 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 60 and 30. Find the height of pillars and the position of thepoint.a lighthouse are 45
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

cloud above the lĂĽkeQl1. 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 60 and 30. Find the height of pillars and the position of thepoint.a lighthouse are 45

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