Question

A flag staff is mounted on the top of a
light house. From a point on the
horizontal ground surface the angle of
elevation of flag staff bottom and top are
found to be 30° and 60° respectively,
Find the height of lighthouse in metres.​

Answer 1

Given : A flag staff is mounted on the top of a light house. From a point on the horizontal ground surface the angle of elevation of flag staff bottom and top are found to be 30° and 60° respectively,

To Find :  the height of lighthouse

Solution:

Let say flag staff height = x  

and  height of lighthouse  = h

d is horizontal distance of point of observation from base of light house

Tan  30°   = h/d      

=> 1/√3 = h/d

=> d  = h√3

Tan  60°   = (h+x)/d      

=> √3 =  (h+x)/d  

=> d  =  (h+x)/√3

Equate d

(h+x)/√3 =  h√3

=> h+x  = 3h

=> 2h = x

=> h = x/2

height of lighthouse is half of the height of flag staff

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Answer 2

Given:-

A flag staff is mounted on the top of a light house. From a point on the horizontal ground surface the angle of elevation of flag staff bottom and top are found to be 30° and 60° respectively,

_________________________________

To Find:-

 

• the height of lighthouse

_________________________________

step-by-step solution:-

let flag staff height be = x

 

and , height of lighthouse be  = 'h'

'd' is horizontal distance of point of observation from base of light house

Tan 30°   = h/d      

→ 1/√3 = h/d

→ d  = h√3

Tan 60°  = (h + x)/d      

→ √3 =  (h+x)/d  

→ d  =  (h + x)/√3

putting the value of 'd' (h√3)

→ (h+x)/√3 =  h√3

→ h+x  = 3h

→ 2h = x

→ h = x/2

Hence , height of lighthouse is half of the height of flag staff.