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Eg:
Calculate the horizontal distance of the tower from stations A & RL at the top of the tower from the following data. The angle readings are taken by observing the top of the tower.
|
Instrument station |
Staff reading on BM |
Angle of elevation |
|
A |
2.750 |
32°15' |
|
B |
2.750 |
27°30' |
BM of staff station P = 345m. The distance between the instrument stations A & B is 30m.
Calculation:
Before drawing over the data given above, let us interpret the question.
1. The staff reading (BS) from stations A and B are the same. This means the RL of the instrument axis is the same for both stations.
2. The angle observed from station A is larger than station B. That means station A is nearer to the tower.
3. We have to calculate the horizontal distance of the building from station A. It means the tower base is inaccessible.
As you can observe in the above drawing,
1. RL of the top of the tower
= [BM at station P + height of instrument axis + height of the top of the tower from instrument axis]
= [ BM + HI + H]
By trigonometric formula,
H = [{d × tan𝝰2 × tan𝝰1 } ÷ (tan𝝰2 - tan𝝰1)]
= [{30m. × tan32°15' × tan27°30' } ÷ (tan32°15' - tan27°30')]
= [{30m. × 0.6309 × 0.5206 } ÷ (0.6309 - 0.5206)]
= [ 9.853 ÷ 0.1103]
H = 89.332m.
Now,
RL of the top of the tower
= [ BM + HI + H]
= [345m. + 2.75m. + 89.332m.]
= 437.082m.
2. Horizontal distance between station A & tower
D =[ d tan𝝰1 ÷ (tan𝝰2 - tan𝝰1)]
= [{30m. × tan27°30' } ÷ (tan32°15' - tan27°30')]
= [{30m. × 0.5206 } ÷ (0.6309 - 0.5206)]
= [ 15.618 ÷ 0.1103]
D = 141.59m.
OR
By trigonometric formula,
tan𝝰2 = [opposite side/adjascent side]
= [H ÷ D]
Therefore,
D = [ H ÷ tan𝝰2]
= [89.332m. ÷ tan32°15']
= [89.332m. ÷ 0.6309]
D = 141.59m. ✔
Continued 👉 Type-3
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Thank you for going through these calculation steps❤. Have a good day 😄.
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