The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower
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55
Answer:
10√3 m
Explanation:
Let the triangle be ABC where AB is the height of the tower and BC is 30 m, while the angle away from the foot is 30°. (/_C = 30° and /_B = 90°)
We need to find the height of th tower i.e. AB.
In ∆ABC
tan C = AB/BC
tan 30° = AB/BC
1/√3 = AB/30
AB = 30/√3
Multiply and divide by √3
AB = 30/√3 × √3/√3
AB = 30√3/3
AB = 10√3 m
Hence, the height of the tower is 10√3 m.
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