the angle of depression of the top and bottom of a 50 m high building from the top of a tower are 45 and 60 find the height of tower
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ANSWER:-
Given:
The angle of depression of the top & bottom of a 50m high building from the top of a tower are 45° & 60° respectively.
To find:
The height of the tower.
Solution:
Let AB be the tower of height h m & CD be the building of height 50m.
•Draw CL perpendicular to AB.
So,
⚫LB= CD= 50m
⚫AL= (h-50)m
⚫LC = BD
Let angle ACL= 45° &
angle ADB= 60°
In ∆ABD,
We know, [tan60° = √3]
In ∆ALC,
We know [tan45°= 1]
Comparing equation (1) & (2), we get;
Thus,
The height of the tower is, h= 118.3m.
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