In tangential tacheometry A theodolite was set up over station... | Civil MCQ | Examoogle

CivilAdvanced Survey

In tangential tacheometry A theodolite was set up over station A · The staff reading taken on station B with vertical angle 5° & 10° are 1m & 3 m respectively so what is horizontal distance AB?

58 m

22.51 m

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option C

22.51 m

Quick Summary:

In tangential tacheometry, hair readings are taken using a theodolite by targeting two different vertical angles to a staff · The horizontal distance $D$ between the instrument station $A$ and staff station $B$ is determined using the staff intercept $s = s_2 - s_1$ and the vertical angles $\theta_1$ and $\theta_2$ . The correct horizontal distance $AB$ for the given staff readings and vertical angles is approximately $22.51\text{ m}$.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$D = \frac{s}{\tan\theta_2 - \tan\theta_1}$ — Horizontal distance when both vertical angles are angles of elevation

$s = S_2 - S_1$ — Staff intercept, where $S_1$ and $S_2$ are upper and lower staff readings

⚙️ Working Principle

When both vertical angles are angles of elevation, the vertical distances to the staff positions are given by $V_1 = D \tan\theta_1$ and $V_2 = D \tan\theta_2$ . The difference between the staff readings gives the staff intercept $s = V_2 - V_1 = D(\tan\theta_2 - \tan\theta_1)$ . Solving for horizontal distance yields $D = \frac{s}{\tan\theta_2 - \tan\theta_1}$ .

📌 Key Points

▸
Tangential tacheometry is used when the instrument transit telescope is not equipped with a stadia diaphragm.
▸
Two vertical angle observations ( $\theta_1$ and $\theta_2$ ) are required for a single staff station.
▸
For two angles of elevation, staff intercept $s = D(\tan\theta_2 - \tan\theta_1)$ , yielding $D = \frac{s}{\tan\theta_2 - \tan\theta_1}$ .

✅ Advantages

▸
Can be performed with a ordinary transit theodolite without stadia hair diaphragm.
▸
Useful for longer sights where stadia wires cannot be clearly resolved.

❌ Disadvantages / Limitations

▸
Requires reading two vertical angles, making measurement slower than stadia method.
▸
Slight error in vertical angle measurement significantly affects the calculated distance.

🛠️ Applications / Uses

▸
Determining horizontal and vertical distances in rough terrain.
▸
Alternative tacheometric method when stadia hair instrument is unavailable.

📄 Additional Information

▸
Calculation: $s = 3\text{ m} - 1\text{ m} = 2\text{ m}$ . $\tan(10°) \approx 0.17633$ and $\tan(5°) \approx 0.08749$ . Difference $= 0.08884$ . Distance $D = 2 / 0.08884 = 22.51\text{ m}$ .
▸
Options A and B ( $58\text{ m}$ ) represent incorrect computation using direct angle differences or improper trigonometric operations.

📊 Diagram / Illustration

✅

C is correct — Using $D = \frac{s}{\tan\theta_2 - \tan\theta_1}$ , the horizontal distance $D = \frac{3-1}{\tan 10°- \tan 5° = 22.51\text{ m}$ .

Core Concepts Used

Click any tag to open in AI Tutor

Tangential Tacheometry Staff Intercept Horizontal Distance Computation

💡 EXAM TIP

Always verify whether both vertical angles are angles of elevation, depression, or one of each, as the denominator sign changes: $D = \frac{s}{\tan\theta_2 + \tan\theta_1}$ when one angle is elevation and the other is depression.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)