Question

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.

Answer 1

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 2

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)