1.20. Trigonometrical Levelling

Try these first

1. 1.

   What is trigonometrical levelling?

   Hint

   Consider the relationship between angles and measurement distances.

2. 2.

   What is the formula to find height using the vertical angle?

   Hint

   Remember the meanings of D and α.

3. 3.

   What is trigonometrical levelling primarily used for?

   • Measuring volumes
   • Measuring angles
   • Determining elevations

   Hint

   Think about surveying techniques.

4. 4.

   True or False: The vertical angle is measured from the object to the horizontal plane.

   • True
   • False

   Hint

   Reconsider the angle measurements’ direction.

5. 5.

   A building stands at the top of a hill 150m away. If the vertical angle to its peak is 45 degrees, what is the height of the building? Assume your instrument is 1.5m high.

   Hint

   Be mindful of the distances and angle used for calculations.

6. 6.

   Two surveyors set positions A and B on flat ground with a distance of 50m between them. From A, they measure an angle of elevation of 40 degrees to the top of a hill; from B, they measure 30 degrees. Calculate the height of the hill above BM, considering the base elevation of 20m.

   Hint

   Use trigonometric identities to relate angles and distances for finding heights.