Question:
The instruments based on trigonometric principles used for tree height measurement are:
The instruments based on trigonometric principles used for tree height measurement are:
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To remember the categories:
- Trigonometric (Angle-based): Abney, Brandis, Haga, Blume-Leiss.
- Geometric (Similar Triangles): Christian, Smythies, Improvised Caliper.
Trigonometric instruments require measuring the horizontal distance to the tree to calculate height.
- Trigonometric (Angle-based): Abney, Brandis, Haga, Blume-Leiss.
- Geometric (Similar Triangles): Christian, Smythies, Improvised Caliper.
Trigonometric instruments require measuring the horizontal distance to the tree to calculate height.
Updated On: Jul 28, 2026
- Brandis hypsometer, Abney's level and Haga altimeter
- Abney's level, Haga altimeter and Improvised calliper
- Christian hypsometer, Improvised calliper and Haga altimeter
- Brandis hypsometer and Christian hypsometer
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Measuring tree height is a key task in forest mensuration.
Height-measuring instruments (hypsometers and altimeters) are classified based on the mathematical principles they use to calculate height: geometric principles (similar triangles) or trigonometric principles.
Step 2: Detailed Explation:
1. Trigonometric Instruments: These instruments use trigonometric relationships (primarily tangent values) to calculate tree height based on the distance from the tree and the angles of elevation/depression to the top and base of the tree:
\[ \text{Height} = D(\tan \theta_1 \pm \tan \theta_2) \]
Instruments in this category contain sighting mechanisms, pendulums, or weighted scales to measure these angles.
Classic examples include the Brandis hypsometer, Abney's level, and Haga altimeter, as well as the Blume-Leiss altimeter and Clinometers.
These instruments are highly accurate and allow for measurements from varying distances.
2. Geometric Instruments: These instruments rely on the properties of similar triangles and do not require measuring angles.
Examples include the Christian hypsometer, Smythies hypsometer, and Improvised caliper.
Therefore, only the instruments in Option (A) are based entirely on trigonometric principles.
Step 3: Fil Answer
The correct set of trigonometric height-measuring instruments is Brandis hypsometer, Abney's level, and Haga altimeter.
Measuring tree height is a key task in forest mensuration.
Height-measuring instruments (hypsometers and altimeters) are classified based on the mathematical principles they use to calculate height: geometric principles (similar triangles) or trigonometric principles.
Step 2: Detailed Explation:
1. Trigonometric Instruments: These instruments use trigonometric relationships (primarily tangent values) to calculate tree height based on the distance from the tree and the angles of elevation/depression to the top and base of the tree:
\[ \text{Height} = D(\tan \theta_1 \pm \tan \theta_2) \]
Instruments in this category contain sighting mechanisms, pendulums, or weighted scales to measure these angles.
Classic examples include the Brandis hypsometer, Abney's level, and Haga altimeter, as well as the Blume-Leiss altimeter and Clinometers.
These instruments are highly accurate and allow for measurements from varying distances.
2. Geometric Instruments: These instruments rely on the properties of similar triangles and do not require measuring angles.
Examples include the Christian hypsometer, Smythies hypsometer, and Improvised caliper.
Therefore, only the instruments in Option (A) are based entirely on trigonometric principles.
Step 3: Fil Answer
The correct set of trigonometric height-measuring instruments is Brandis hypsometer, Abney's level, and Haga altimeter.
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