Mathematics
The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower, when seen from the top of the second tower is 30°. If the height of the second tower is 60 m, find the height of the first tower.
Heights & Distances
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Answer
Let AB be the first tower and CD be the second tower. From C draw a line parallel to AD and perpendicular to AB meeting AB at point E.
Now ADCE forms a rectangle,
EC = AD = 140
AE = DC = 60.
Considering right angled △BCE, we get
From figure,
AB = AE + BE = 60 + 80.83 = 140.83
Hence, the height of the first tower is 140.83 meters.
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