Question

a flag pole is fitted in the wall. The angle of elevation of flag pole ends made by a person standing on the other side of a 40m wide road is 60 and 45 respectively.the length( hight). of flag pole is

Answer 1

See attachment, a rough daigram as shown .
assume height of flag pole is h.

From triangle ABC ,
tan60° = AB/BC
AB = height of flag pole + A part of height of wall {assume x }
AB = h + x
BC = 40m

Now , tan60° = (h + x)/40
⇒√3 = (h + x)/40
⇒ 40√3 = h + x -------(1)

Now, from ∆DBC
tan45° = DB/BC
⇒ 1 = x/40
⇒ x = 40m , put it in equation (1)

Now, 40√3 = h + 40
h = 40√3 - 40

Hence, height of pole is 40(√3 - 1) m

Answer 2

HELLO DEAR,


let

AD = h (height of flag pole)

BC = 40m

<x = 45°

<y = 60°

BD = h' =  A part of height of wall 

AB = AD + BD = (h + h')


now,


IN∆ABC ,

AB / BC = tanx


⇒ (h + h') / 40 = tan60°


⇒ (h + h') / 40 = √3


⇒(h + h') = 40√3-----------(1)



now, IN ∆ DBC


DB / BC = tan45°


⇒h' / 40 = 1


⇒h' = 40m put in-----(1)


we get,


(h + 40) = 40√3


⇒ h = 40√3 - 40


⇒h = 40(√3 - 1)m

or


⇒h = 40(1.732 - 1)


⇒h = 40(0.732)


⇒h = 29.28m(approx)



HENCE, the height of pole is 40(√3 - 1)m or 29.28m




I HOPE ITS HELP YOU DEAR,
THANKS