Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Which of the following indicates the value of D, when base of object is accessible?
= h cot ╬▒
= h / tan ╬▒
= tan ╬▒ / h
Both A and B
Both A and B
In trigonometrical levelling, when the base of an object is accessible, the horizontal distance D between the instrument station and the object can be directly determined using simple right-angle trigonometry. If h is the vertical height of the object above the instrument axis and ╬▒ is the angle of elevation, then tan╬▒=DhтАЛ, which gives D=tan╬▒hтАЛ=hcot╬▒.
In trigonometrical levelling, when the base of an object is accessible, the horizontal distance D between the instrument station and the object can be directly determined using simple right-angle trigonometry. If h is the vertical height of the object above the instrument axis and ╬▒ is the angle of elevation, then tan╬▒=DhтАЛ, which gives D=tan╬▒hтАЛ=hcot╬▒.
D=tan╬▒hтАЛ тАФ Horizontal distance in terms of tangent
D=hcot╬▒ тАФ Horizontal distance in terms of cotangent
h=Dtan╬▒ тАФ Vertical height above instrument axis
The horizontal distance is determined by measuring the angle of elevation ╬▒ using a theodolite set up at an instrument station at a known horizontal plane. Since the base is accessible, the line of sight forms a right-angled triangle with the vertical height h and horizontal distance D. Utilizing trigonometric identities, D can be expressed either as hcot╬▒ or tan╬▒hтАЛ, both being mathematically identical.
Base of the object is accessible, meaning horizontal distance D can be measured directly or calculated from a single station setup.
cot╬▒ is the reciprocal of tan╬▒, making hcot╬▒ and tan╬▒hтАЛ identical mathematical expressions.
Trigonometrical levelling relies on measuring vertical angles and known horizontal distances to compute elevations.
Requires only one instrument station setup when the base is accessible.
Provides quick and precise determination of height and distance using basic trigonometric relations.
Assumes the base is on accessible ground where horizontal sighting is unobstructed.
Refraction and curvature corrections must be applied for long distances.
Determining heights of towers, chimneys, or buildings when access to the base is available.
Topographical surveying and indirect levelling in hilly terrain.
Option A (hcot╬▒) and Option B (tan╬▒hтАЛ) are trigonometric equivalents since cot╬▒=tan╬▒1тАЛ.
Option C (htan╬▒тАЛ) represents D1тАЛ, which is mathematically incorrect for calculating distance D.
D is correct тАФ Both hcot╬▒ and tan╬▒hтАЛ represent the accurate formula for distance D when the base of the object is accessible.
In competitive exams, always check for reciprocal trigonometric forms (like tan vs cot) before selecting single-option answers to avoid missing 'Both A and B' choices.