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Triangulation

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Question Bank: t65

MSTE - Surveying / Triangulation / Civil Engineering Refresher

Triangulation distances: AB = 1200 m, AC = 965 m. Angles at boat F are 28°15' and 22°30'. Find distance FB.

  1. 1875.2 m
  2. 2535.3 m
  3. 1540.5 m
  4. 1200.0 m

Solution pending in psadquestions/t65.json.

Question Bank: w182

MSTE - Surveying / Triangulation / MSTE May 2022

In hilly or mountainous terrain, it is often difficult to determine heights. A geologist took measurements at two points B and C, 928 m apart. The angle of elevation from B to the top of the mountain at A is 47°10′. The angle of elevation from C to B is 8°40′, and the angle of elevation from C to A is 32°30′. It is known that the elevation at C is 1621 m to the nearest meter. What is the elevation at A?

  1. 2921 m
  2. 2847 m
  3. 2893 m
  4. 2524 m
The angle at $B$ in triangle $CBA$ is $180^\circ-47^\circ10'-8^\circ40'=124^\circ10'$, and the remaining angle is $23^\circ20'$. By the sine law, $$\frac{AC}{\sin124^\circ10'}=\frac{928}{\sin23^\circ20'},$$ giving $AC\approx1938$ m. The vertical rise is $$H=AC\sin32^\circ30'\approx1224\text{ m}.$$ Adding the elevation at $C$ gives about $1621+1224=2845$ m, corresponding to 2847 m.