Question

the height of Tower is half the height of the flagstaff on it and the angle of elevation of the top of the tower has seen from the point on the ground is 30 find the angle of elevation of the top of the flagstaff as seen from the same point

Answer 1

let the height of tower be AB = h m. let AD be the hoarding such that AD = 5 m

let C be the observation point. 

such that the angle of elevation of the top of the hoarding i.e. ∠BCD= 60 deg.

the angle of depression of the observation point C from A be ∠PAC=∠ACB = 45 deg.

therefore in the triangle ABC, 

tan 45° = AB BC 
1 =  h BC ⇒ BC = h m ...........(1)

In the triangle DBC,

tan 60° = DB BC 
√3 =  h+5 h   [DB = DA + AB = 5 + h]
√3h = h + 5
(√3 - 1)h = 5

h =  5 3 - 1 = 5 3 -1 × 3 +1 3 +1

h =  5( 3 +1) 2 =  5 2 (1.732+1) = 5 2 × 2.73 
h = 6.825 m
thus the height of the tower is 6.825 m 

Answer 2

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