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Eg:
Calculate the horizontal distance of the tower from station A & RL of 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 station A & B is 30m.
Calculation:
Before making a drawing over the above-given data, let us interpret the question.
1. Staff reading (BS) from stations A & B are the same. It means the RL of the instrument axis is the same for both stations.
2. Angle observed from station A is larger than station B. It 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 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 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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