A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.
Answers
Answer:
The height of the tower is 70 m and height of the flagstaff is 51.24 m.
Step-by-step explanation:
Given :
Distance from the tower and an observer, CD = 70 m
Angle of elevation from the top of the flagstaff (θ), ∠ADC = 60°
Angle of elevation from the bottom of the flagstaff ,(θ), ∠BDC = 45°
Height of flag staff, AB = y m
Height of tower ,BC = x m
In right angle triangle, ∆BCD ,
tan θ = P/ B
tan 45° = BC/CD
1 = x /70
x = 70 m
In right angle triangle, ∆ADC,
tan θ = P/ B
tan 60° = AC/CD
√3 = (AB + BC)/CD
√3 = (y + x)/70
√3 = (y + 70)/70
70√3 = y + 70
y = 70√3 - 70
y = 70(√3 - 1)
y = 70(1.732 - 1)
[√3 = 1.732]
y = 70 × 0.732
y = 51.24 m
Hence, the height of the tower is 70 m and height of the flagstaff is 51.24 m.
HOPE THIS ANSWER WILL HELP YOU…
Answer:
let height of tower be h and hight of flag staff = x
Step-by-step explanation:
tan60° =( h +x)/70
70√3 = h + x ---(1)
tan45° = h/70
h = 70
from (1) x = 70√3 - 70
= 70(√3 - 1)
required answers ,
height of tower = 70m and height of
flag staff =70(√3-1)