1

HP-35 How-To Online Course

PROGRAMS COVERED

• Area by Coordinates• Azimuth Bearing• Triangles• Intersections

• H & V Curves• Inversing

– Standard– Radial

• Stubbing• Traversing

AREA BY COORDINATES

1

2

3

2

AREA BY COORDINATES

)*()*)(*()*)(*()*)(*()*)(*(*2

4145342312

14433221

YXYXYXYXYXYXYXYXYXA

AREA BY COORDINATES• XEQ A• -25 R/S• 25 R/S• 35 R/S• 15 R/S• 20 R/S• 5 R/S

• -20 R/S• 5 R/S

• -25 R/S• 25 R/S

ANGLE CONVERSIONS

• Bearing->Azimuth

• Azimuth->Bearing

• DMS to DD

4

5

6

3

AZIMUTHBEARING

BEARING->AZIMUTH

• Tiny Tim is retracing a survey from the early 1950’s. Unfortunately, he just realized that his total station traverse is in azimuths while the original survey is in bearings. What are the azimuths for the given bearings?– N32E S82W S82-92-19W

BEARING->AZIMUTH

• What are the azimuths for the given bearings?– N32E– S82W– S82-42-19W

• XEQ B

• 32 R/S• 1 R/S

• PRESTO!• A = 32

7

8

9

4

BEARING->AZIMUTH• XEQ B

• 32 R/S• 1 R/S

• PRESTO!• A = 32

• XEQ B

• 82 R/S• 3 R/S

• PRESTO!• A = 262

• XEQ B

• 82.4219 R/S

• 3 R/S

• PRESTO!• A =

BEARING->AZIMUTH• XEQ B• 39-39-12 R/S• 1 R/S• [read azimuth] R/S

• XEQ B• 44-22-55 R/S• 3 R/S• [read azimuth] R/S

• N39-39-12E to AZ

• S44-22-55W to AZ

AZIMUTH->BEARING

• Jimmy John is a student in a 4-year surveying program. As part of a national competition, the students have been asked to use a compass & chain to perform a historic survey. Luckily, he surveyed the same points as a student last year with a total station. He wants to compare his compass survey with the total station traverse. Help him convert the following azimuths to bearings: 293-21-19, 118-11-59, 092-22-21

10

11

12

5

AZIMUTH->BEARING

• Help him convert the following azimuths to bearings: – 293-21-19– 118-11-59– 092-22-21

• XEQ Q

• 293.2119 R/S

• PRESTO!• B = 66-38-41 R/S• Q = 4

AZIMUTH->BEARING• XEQ Q

• 293.2119 R/S

• PRESTO!• B = 66-38-41

R/S• Q = 4

• XEQ Q

• 118-11-59 R/S

• PRESTO!• B = 61-48-01

R/S• Q = 2

• XEQ Q

• 092-22-21 R/S

• PRESTO!• B = 87-37-39

R/S• Q = 2

TRIANGLES, TRIANGLES, TRIANGLES, TRIANGLES!

• SSS• SAS• SAA• ASA• SSA

13

14

15

6

ONLINE TRIANGLE SOLVER

https://www.calculator.net/triangle-calculator.html

TRIANGLESSIDE-SIDE-SIDE

SIDE-SIDE-SIDE TRIANGLES

"SSS" is when we know three sides of the triangle, and want to

find the missing angles

cos(C) = a2 + b2 − c2 / 2abcos(A) = b2 + c2 − a2 / 2bccos(B) = c2 + a2 − b2 / 2ca

16

17

18

7

SIDE-SIDE-SIDE TRIANGLESA traverse is observed with a differential level, only able to measure rough distances. To verify the accuracy of the total station reading last week, your boss asks you to compute the interior angles of the 3-sided

traverse. The triangle measures 1029.39, 993.28 and 897.27 What do you

report back?

• XEQ C ENTER

• 1029.39 R/S

• 993.28 R/S

• 897.27 R/S

SIDE-SIDE-SIDE TRIANGLESINPUT

• XEQ C

• 1029.39 R/S• 993.28 R/S • 897.27 R/S

• PRESTO!• 65.4506/1029.39 R/S• 61.3701/993.28 R/S• 52.3754/897.27

OUTPUT

• ANGLE OPP & SIDE 1 DIST

• ANGLE OPP & SIDE 2 DIST

• ANGLE OPP & SIDE 3 DIST

• TRIANGLE AREA

TRIANGLESSIDE-ANGLE-SIDE

19

20

21

8

SIDE-ANGLE-SIDE TRIANGLES

"SAS" is when we know two sides and the

angle between them.

a2 = b2 + c2 − 2bc cosA

SIDE-ANGLE-SIDE TRIANGLES

The City of Nowhere has mandated that all flagpoles must not exceed a

height of 49.50’ because the city revenue needs a shot in the arm. You, Super Surveyor, have been

asked to survey all 595,393 flagpoles in the city. Since you don’t enjoy

climbing, you have decided to use your total station. On flagpole

393,232, the measurements include: bottom of 49.49’, top of 66.32’ and angle of 45 degrees. What’s the

height of the flagpole?

• XEQ D ENTER

• 49.49 R/S

• 45 R/S

• 66.32 R/S

SIDE-ANGLE-SIDE TRIANGLESINPUT

• XEQ D ENTER

• 66.32 R/S

• 45 R/S

• 49.49 R/S

OUTPUT

• 48.1000 / 49.49

• 86.4959 / 66.32

• 45.0000 / 46.97

22

23

24

9

TRIANGLESSIDE-ANGLE-ANGLE

SIDE-ANGLE-ANGLE TRIANGLES

“AAS” is when we know two angles and

one side (which is not between the

angles)𝐴 𝐵 𝐶 180

+ +

SIDE-ANGLE-ANGLE TRIANGLES

• Solve the following triangle • XEQ E ENTER

• 7 R/S

• 35 R/S

• 62 R/S

25

26

27

10

SIDE-ANGLE-ANGLE TRIANGLESINPUT

• XEQ E ENTER

• 7 R/S

• 35 R/S

• 62 R/S

OUTPUT

• 62.0000 / 7

• 83.0000 / 7.8689

• 35.0000 / 4.5473

TRIANGLESANGLE-SIDE-ANGLE

ANGLE-SIDE-ANGLE TRIANGLES

"ASA" is when we know two angles

and a side between the

angles𝐴 𝐵 𝐶 180

+ +

28

29

30

11

ANGLE-SIDE-ANGLE TRIANGLESA total station traverse was performed

on Cranky Customer’s residential lot last week. But apparently, the data collector

was acting-up. It collected the angle between the SE corner and the N corner

as 64-15-35 degrees and the angle between the SW corner and the N corner as 53-44-50 degrees. Luckily, you also got the distance between the SE and

SW corners at 954.49’. What’s the distance from the SE to N and SW to N

corners?

• XEQ F ENTER

• 64-15-35 R/S

• 954.49 R/S

• 53-44-50 R/S

TRIANGLESSIDE-SIDE-ANGLE

ANGLE-SIDE-ANGLE TRIANGLESINPUT

• XEQ F ENTER

• 64-15-35 R/S

• 954.49 R/S

• 53-44-50 R/S

OUTPUT

• 61.5935 / 954.49

• 64.1535 / 973.821

• 53.4450 / 871.7134

31

32

33

12

SIDE-SIDE-ANGLE TRIANGLES

"SSA" is when we know two sides

and an angle that is not the angle

between the sides𝐴 𝐵 𝐶 180

+ +

SIDE-SIDE-ANGLE TRIANGLES• Solve This Triangle: • XEQ G ENTER

• 8 R/S

• 13 R/S

• 31-00-00 R/S

SIDE-SIDE-ANGLE TRIANGLESINPUT

• XEQ G ENTER

• 8 R/S

• 13 R/S

• 31-00-00 R/S

SOLUTION 1

• 31-00-00 / 8.0

• 56-49-05 / 13.0

• 92-10-55 / 15.522

34

35

36

13

INTERSECTIONS

INTERSECTIONS

• Angle-Angle

• Angle-Distance

• Distance-Distance

ANGLE-ANGLE

• Angle-Angle intersections provide the location of an intersection between two azimuths – bearings -interior angles and the distance from the intersection to either of the original points.

37

38

39

14

ANGLE-ANGLE

ANGLE-ANGLEInput

• N1 = 78• E1 = 21• N2 = 128• E1 = 512• Azimuth 1 = 72• Azimuth 2 = 301

Output

• N of Intersection• E of Intersection

• Dist from PT 1 to Int

• Dist from PT 2 to Int

ANGLE-ANGLEInput

• XEQ L• 21 R/S• 78 R/S• 72 R/S• 512 R/S• 128 R/S• 301 R/S

Output

• E = 393.68• N = 199.09

• Dist 1 = 391.86• Dist 2 = 138.03

• DONE!

40

41

42

15

ANGLE-DISTANCE

• Angle-Distance intersections provide the location of an intersection between one azimuth and one distance and provide the X/Y coordinates of the intersection as well as the distance from the intersection to either of the original points.

ANGLE-DISTANCE

ANGLE-DISTANCEInput

• X1 = 78• Y1 = 21

• X2 = 128• Y1 = 512

• Azimuth 1 = 72• Distance 2 = 510.25

Output• X-CRD of Int 1• Y-CRD of Int 1• Azimuth to Int 1• Dist to Int 1

• X-CRD of Int 2• Y-CRD of Int 2• Azimuth to Int 2• Dist to Int 2

43

44

45

16

ANGLE-DISTANCEInput

• XEQ L• 78 R/S• 21 R/S• 72 R/S• 128 R/S• 512 R/S• 510.25 R/S

Output

• X = 493.56• Y = 156.02• Z = 134.14• S = 436.94

X = 41.48Y = 9.14

Z = 189.45S = 38.39

DONE!

DISTANCE-DISTANCE

• Distance-Distance intersections provide the location of two intersections between two distances (X&Y) and the azimuths from the two intersection to either of the original points.

DISTANCE-DISTANCE

46

47

48

17

DISTANCE-DISTANCEInput

• X1 = 0• Y1 = 0• R = 500

• X2 = 500• Y1 = 0• R = 500

Output• X = 250• Y = -433.01• Z = 150-00-00• Z = 210-00-00

• X = 250• Y = 433.01• Z = 30-00-00• Z = 330-00-00

DISTANCE-DISTANCEInput

• XEQ N• 0 R/S• 0 R/S• 500 R/S

• 500 R/S• 0 R/S• 500 R/S

Output• X = 250• Y = -433.01• Z = 150-00-00• Z = 210-00-00

• X = 250• Y = 433.01• Z = 30-00-00• Z = 330-00-00

VERTICLE & HORIZONTAL AND CURVES

49

50

51

18

CURVES

• Horizontal

• Vertical

HORIZONTAL CURVES

HORIZONTAL CURVESREQUIRED (1+)

• Delta Angle

• Degree of Curvature

• Radius

OPTIONAL (2+)

• Tangent• Curve Length• Chord Length• Middle-Ordinate• External Distance

52

53

54

19

HORIZONTAL CURVE PROBLEM

• Compute R, L and E for a horizontal curve with a tangent of 75’ a central angle of 28° and a PI of 08+00

HORIZONTAL CURVE PROBLEM

• Compute R, L and E

• Tangent 75 • Central angle of 28°• PI of 08+00

• XEQ H

• R/S• 28 R/S• 75 R/S• R/S• R/S• R/S• R/S• R/S• R/S• R/S• R/S• 800 R/S• R/S

• PRESTO!

• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S• READ # R/S

VERTICAL CURVES

55

56

57

20

VERTICAL CURVESINPUTS

• PVI Station + Elev

• G1 and G2

• L

• Sta Inc

OUTPUTS

• High/Low Point (Elev + Sta)

• Elev @ Sta

VERTICAL CURVE PROBLEM

• Given an equal-tangent vertical curve with a g1 of +2.20%, g2 of -3.10%, length of 350’ and PVI of 12+50 @ 1000’, what is the station and elevation of the PC?

VERTICAL CURVE PROBLEM

• g1 of +2.20%, • g2 of -3.10%, • length of 350’ • PVI of 12+50 @

1000

• XEQ V

• 1250 R/S• 1000 R/S• 2.2 R/S• -3.1 R/S• 350 R/S

• PRESTO!• (ANY) R/S• S = 1075 R/S• E = 996.15

58

59

60

21

RADIALINVERSE

Radial Inverse

Radial Inverse

61

62

63

22

Radial Inverse

Using azimuth/distance, any point can be found radiating from the initial point.

Traverse Inverse

64

65

66

23

Traverse Inverse

Traverse Inverse

Traverse Inverse

67

68

69

24

Traverse Inverse

INVERSING AND STUBBING

• An inverse finds the azimuth/distance between two known points (X & Y)

• A stub finds Point #2’s X & Y coordinates from Point #1 and an azimuth/distance

INVERSING BETWEEN POINTS

• XEQ I

• 5000 R/S• 200 R/S• 1500 R/S• 5350 R/S

• PRESTO!• D = 6226.7568 R/S• A = 124.1202 (DMS)

70

71

72

25

LOCATING A POINT BY STUBBING• XEQ S

• 500 R/S• 200 R/S• 88.3902 R/S• 505.22 R/S

• PRESTO!• X = 705.0799• R/S• Y = 511.898

DMS TO DD– Sally has a problem. She is working with

trig functions using a set of survey angles. Unfortunately, you cannot use D-M-S formatted numbers for the SIN, COS and TAN functions. You must convert those numbers to DD and then run the trig functions. Can you help her? Find the following numbers in DD format:

– 293-21-19 118-11-59 092-22-21

DMS TO DD

– Can you help her convert these numbers to DD?

– 293-21-19 – 118-11-59 – 092-22-21

• 293.2119

• Gold + 8 (->HMS)

• Enter

• PRESTO• 293 1248 (293-12-

73

74

75

26

DMS TO DD• 293.2119

• Gold + 8 (->HMS)

• Enter

• PRESTO• 293.1248 (293-

12-48)

• 118.1159

• Gold + 8 (->HMS)

• Enter

• PRESTO• 118.0657 (118-06-

57)

• 092.2221

• Gold + 8 (->HMS)

• Enter

• PRESTO• 92.1320 (92-13-20)

76