A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff. At a point on the plane 70m away from the tower, an observer notice that the angle of elevation of the top and the bottom of the flag staff are respectively 60* and 45*. Find the height of the flag staff and that of the tower.
Answers
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Solution:
Given:
➜ A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff.
➜ At a point on the plane 70m away from the tower,an observer notice that the angle of elevation of the top and the bottom of the flag staff are respectively 60° and 45°.
Find:
➜ Find the height of the flag staff and that of the tower.
According to the given question:
➜ 70 m = BC.
➜ BC = Distance between observer and tower.
➜ 45° = angle of elevation of bottom of the flag staff and 60° is the angle of elevation of top of the flag staff.
➜ Let "h" the height of the flag staff = AB.
Calculations:
➜ tan θ = Opposite side
---------------------
Adjacent side
➜ tan 45° = AB
-----
BC
➜ 1 = H
-----
170
➜ H = 70
➜ tan 60° = DB
-----
BC
➜ √3 = AD + AB ( h + H )
------------- = ----------------
70 70
➜ h + 70 = 70 √3
➜ h = 70 (√3 - 1)
➜ h = 70 (1.732 - 1)
➜ h = 51.24 m
Therefore, 70m is the height of tower and 51.24 is the height of flag staff.