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Angles and Directions

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Problem:

The magnetic bearing of line AB was recorded as S43°30'E in 1888. If the magnetic declination was 2°00'E, what is the astronomic bearing of the line? If the declination is now 3°00'W, what is the magnetic bearing of the line today?

Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram Angles and Directions | Bearings and Azimuths – Problem 1: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram Angles and Directions | Bearings and Azimuths – Problem 2: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram Angles and Directions | Bearings and Azimuths – Problem 3: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 5: – Diagram Angles and Directions | Bearings and Azimuths – Problem 5: – Diagram Angles and Directions | Bearings and Azimuths – Problem 5: – Diagram Angles and Directions | Bearings and Azimuths – Problem 5: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 6: – Diagram Angles and Directions | Bearings and Azimuths – Problem 6: – Diagram Angles and Directions | Bearings and Azimuths – Problem 6: – Diagram Angles and Directions | Bearings and Azimuths – Problem 6: – Diagram

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Angles and Directions | Bearings and Azimuths – Problem 8: – Diagram Angles and Directions | Bearings and Azimuths – Problem 8: – Diagram Angles and Directions | Bearings and Azimuths – Problem 8: – Diagram Angles and Directions | Bearings and Azimuths – Problem 8: – Diagram
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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: t66

MSTE - Surveying / Area Computation / Civil Engineering Refresher

A four-sided tract ABCD is surveyed from internal point P. PA = 420.35 m, PB = 530.15 m, PC = 480.75 m, PD = 695.10 m. Angles APB = 78.5°, BPC = 72°, CPD = 130.25°. Find the area in hectares.

  1. 50.16 hectares
  2. 45.20 hectares
  3. 55.80 hectares
  4. 60.30 hectares
Divide the tract into triangles from internal point P. The missing angle is:
$\angle DPA = 360^\circ - 78.5^\circ - 72^\circ - 130.25^\circ = 79.25^\circ$
Use $A = \frac{1}{2}ab\sin C$ for each triangle:
$A = \frac{1}{2}[420.35(530.15)\sin78.5^\circ + 530.15(480.75)\sin72^\circ + 480.75(695.10)\sin130.25^\circ + 695.10(420.35)\sin79.25^\circ]$
$A \approx 501,600\text{ m}^2$
$\boxed{A = 50.16\text{ hectares}}$

Question Bank: t1126

MSTE - Surveying / Measurements and Areas / Gemini mapped Chapter 7 to 10

Given a regular octagonal lot ABCDEFGH. If the bearing of side AB is N 18° W, what is the bearing of side DE?

  1. S 66° E
  2. S 60° E
  3. S 63° E
  4. S 68° E

Solution pending in psadquestions/t1126.json.

Question Bank: t1133

MSTE - Surveying / Measurements and Areas / Gemini mapped Chapter 7 to 10

A triangular parcel ABC have the following technical description: [SIDE AB: BEARING N 60° 30' W, LENGTH 68.75 m; BC: N 80° 30' E, LENGTH 125.90 m; CA: ?, ?]. Determine the following:

The bearing of side CA.

  1. S 45° 12' W
  2. S 57° 45' W
  3. S 52° 34' W
  4. S 49° 40' W

The length of side CA.

  1. 65.3 m
  2. 103.8 m
  3. 93.4 m
  4. 84.4 m

Solution pending in psadquestions/t1133.json.

Question Bank: w116

MSTE - Surveying / Surveying / MSTE November 2021

An engineer measures 280 m from point A to point C in a direction perpendicular to segment AB. At C, the angle ACB is 49°50′. How long should the bridge AB be?

  1. 331.73 m
  2. 287.25 m
  3. 356.96 m
  4. 314.17 m
In right triangle $ACB$, $AB=AC\tan(\angle ACB)=280\tan49°50'\approx331.73$ m.

Question Bank: w118

MSTE - Surveying / Surveying / MSTE November 2021

The angle of elevation of the top of a tower from point A on the ground is 19.9°. Point B, 50 feet closer to the tower, has an angle of elevation of 21.8°. What is the height of the tower?

  1. 161 ft
  2. 171 ft
  3. 191 ft
  4. 181 ft
With tower height $h$, $\frac{h}{\tan19.9°}-\frac{h}{\tan21.8°}=50$. Solving gives $h\approx190.6$ ft, or about 191 ft.

Question Bank: w120

MSTE - Surveying / Surveying / MSTE November 2021

From a point Q on the ground of a square courtyard with area 160,000 square feet, the angles of elevation of three equal-height flagstaffs at three consecutive corners A, B, and C are 45°, 60°, and 60°, respectively. Find the height of each flagstaff in meters.

  1. 149.58
  2. 114.32
  3. 136.78
  4. 125.47
The square side is $\sqrt{160000}=400$ ft. From the elevation angles, the horizontal distances are $h\cot45°=h$ and $h\cot60°=0.577h$. Using the square geometry gives $h\approx114.3$ m.