Question

two pillars of equal height stand on either side of a roadway which is 150 m wide
at a point in the roadway between the pillars the elevation of the tops of the pillar are 60 degree and 30 degree find the height of the pillars and the position of the point

Answer 1

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 pillars is 37.5√3 m

Step-by-step explanation:

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Answer 2

Answer:

37.5√3 M

Step-by-step explanation:

let x be the position of the point.

tan30° = h/x => h = x/√3--(1)

tan 60° = h /150-x

h = (150-x ) × √3 --(2)

equalise (1) & (2) then we have

x/√3 = (150-x) × √3

x = 450 - 3x => 4x = 450

x = 112.5m

from(2) h = (150-112.5) × √3

= 37.5 √3 m