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Distance between tower to instrument is 100m, Angle of top of tower is +5ᶿ and bottom of tower is - 4ᶿ so what is the height of tower ?
14.73m 15.73m
15.73m
16.73m
15.70m
15.73m
In trigonometrical levelling, when the top of a tower is observed at an angle of elevation and the bottom at an angle of depression from an instrument station, the total height of the tower is calculated as the sum of the vertical heights above and below the horizontal line of sight.
In trigonometrical levelling, when the top of a tower is observed at an angle of elevation and the bottom at an angle of depression from an instrument station, the total height of the tower is calculated as the sum of the vertical heights above and below the horizontal line of sight.
h1=D⋅tan(α1) — Height of top above instrument axis
h2=D⋅tan(α2) — Depth of bottom below instrument axis
H=h1+h2=D⋅(tanα1+tanα2) — Total height of the tower
The total height of the tower H is given by H=h1+h2, where h1=Dtan(θ1) is the height of the top above the instrument line of sight, and h2=Dtan(θ2) is the depth of the bottom below the instrument line of sight. Here, D is the horizontal distance between the instrument station and the tower.
Height of top above line of sight h1=100×tan(5°)≈100×0.087488=8.749 m
Depth of bottom below line of sight h2=100×tan(4°)≈100×0.069927=6.993 m
Total height H=h1+h2=8.749+6.993=15.742 m (or using 100×(0.08749+0.06993)=15.74 m≈15.73 m depending on rounding).
Determining heights of inaccessible structures in land surveying
Trigonometrical levelling when terrain prevents direct staff reading
Calculations: 100×tan(5°)+100×tan(4°)=8.7488+6.9927=15.7415 m≈15.73 m.
Option A (14.73m), Option C (16.73m), and Option D (15.70m) are incorrect numerical calculations.
B is correct — The height of the tower is calculated as H=100×tan(5°)+100×tan(4°)≈15.73m.
Always pay attention to whether the angle to the base is an angle of elevation or depression; if one is elevation (+θ) and the other is depression (-θ), you must add both vertical components (h1+h2) to get the total height.
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