Angle of elevation of the top of the tower from a point on the ground which is 30m away root of the tower is 30 degree . Find the height of the tower
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Answer:
Height of the tower = 10√3 meters
Step-by-step explanation:
SEE THE FIGURE FOR REFERENCE
Angle of elevation = 30 deg
Distance of point from tower = 30 m
Now, we have ΔABC
AB represents the height of the tower
BC represents the distance of point away from foot of the tower
we have,
tan θ = AB / BC ...(Opposite side / adjacent side)
as θ = 30 deg
tan (30)deg = AB / 30 ...(Since BC = 30m)
1/√3 = AB / 30 ...(Since tan 30 deg = 1/√3 )
AB = 30/√3
AB = 10√3 meters
Thus height of the tower = 10√3 meters
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Answered by
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Answer:
In ∆ ABC,
tan 30° = AB/BC
1/√3 = AB/30
30/√3 = AB
AB = 30/√3
Now, Multiplying numerator and denominator by 3 we get:
AB = 30/√3 × √3/√3
AB = 30√3/3
AB = 10√3
Therefore, the height of the tower is 10√3.
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