Triangle Solutions

Description

Origin: HP-34C MATHEMATICS Applications, June 1981, p. 33

This program may be used to find the sides, the angles, and the area of a plane triangle.

In general, the specification of any three of the six parameters of a triangle (3 sides, 3 angles) is sufficient to define the triangle. (The exception is that three angles will not define a triangle.) There are thus five possible cases that this program will handle: two sides and the included angle (SAS), two angles and the included side (ASA), two sides and the adjacent angle (SSA—an ambiguous case), two angles and the adjacent side (AAS), and three sides (SSS).

If the three known input values are selected in a clockwise order around the triangle the outputs will also follow a clockwise order. The outputs are obtained by reviewing the storage registers as follows:

Remarks:
Instructions:
  1. SSS: 3 sides known
  2. ASA: 2 angles and included side known
  3. SAA: 2 angles and adjacent side known
  4. SAS: 2 sides and included angle known
  5. SSA: 2 sides and adjacent angle known
Note: The following examples are calculated with "Strict HP-15C behaviour" activated. When deactivated, results will differ slightly.

Example 1:

A surveyor is to find the area and dimensions of a triangular land parcel. From point A, the distance to B and C are measured with an electronic distance meter. The angle between AB and AC is also measure. Find the area and the dimensions of the triangle.

This is a side-angle-side problem where:
S1 = 171.63, A1 = 98°12' and S2 = 297.35.

g DEG f FIX 2
171.63 ENTER → 171.63
98.12 g →H → 98.20
297.35 GSB 4 → 25,281.69
RCL 4 → 27.80
RCL 5 → 364.18
RCL 6 → 54:00

Example 2:

Given 2 sides and a nonincluded angle solve for the triangle:

Side1 = 25.6
Side2 = 32.8
Angle2 = 42.3°

25.6 ENTER → 25.60
32.9 ENTER → 32.80
42.3 GSB 5 → 2 (2 Solutions - flashing)
R/S RCL 0 → 410.85 (Area 1)
A → 124.68 (Area 2)
RCL 1 → 26.60 (Area 2)
etc.

Program Resources

Labels

Name Description Name Description
 A Calculates 2nd solution (if available)  4 SAS: 2 sides and included angle known
 E # Set flashing for solution indicator  5 SSA: 2 sides and adjacent angle known
 0 #  7 # Indicator 2 solutions
 1 SSS: 3 sides known  8 # Calculate adjacent angle
 2 ASA: 2 angles and included side known  9 # Indicator 1 solution
 3 SAA: 2 angles and adjacent side known

Storage Registers

Name Description
 0 Area
 1 Side 1
 2 Angle 1
 3 Side 2
 4 Angle 2
 5 Side 3
 6 Angle 3

Flags

Number Description
9 Flashing display indicates number of solutions found

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000 045 45 2 RCL 2 090 42,21, 4 f LBL 4
001 42,21, 1 f LBL 1 046 40 + 091 44 3 STO 3
002 44 5 STO 5 047 23 SIN 092 33 R⬇
003 33 R⬇ 048 45 4 RCL 4 093 44 2 STO 2
004 44 3 STO 3 049 23 SIN 094 33 R⬇
005 33 R⬇ 050 10 ÷ 095 44 1 STO 1
006 44 1 STO 1 051 45 1 RCL 1 096 42,21, 0 f LBL 0
007 45 3 RCL 3 052 20 × 097 45 2 RCL 2
008 43 1 g →P 053 44 3 STO 3 098 45 1 RCL 1
009 43 11 g 054 22 0 GTO 0 099 42 1 f → R
010 45 5 RCL 5 055 42,21, 5 f LBL 5 100 45 3 RCL 3
011 43 11 g 056 44 4 STO 4 101 34 x↔y
012 30 057 33 R⬇ 102 30
013 45 1 RCL 1 058 44 3 STO 3 103 43 1 g →P
014 45 3 RCL 3 059 33 R⬇ 104 44 5 STO 5
015 20 × 060 44 1 STO 1 105 34 x↔y
016 2 2 061 45 3 RCL 3 106 44 4 STO 4
017 20 × 062 45 4 RCL 4 107 45 2 RCL 2
018 10 ÷ 063 23 SIN 108 40 +
019 43 24 g COS⁻¹ 064 45 1 RCL 1 109 32 9 GSB 9
020 44 2 STO 2 065 10 ÷ 110 44 6 STO 6
021 22 0 GTO 0 066 20 × 111 23 SIN
022 42,21, 2 f LBL 2 067 43 23 g SIN⁻¹ 112 20 ×
023 44 2 STO 2 068 45 4 RCL 4 113 45 1 RCL 1
024 33 R⬇ 069 40 + 114 20 ×
025 44 1 STO 1 070 32 9 GSB 9 115 2 2
026 33 R⬇ 071 44 2 STO 2 116 10 ÷
027 44 6 STO 6 072 32 0 GSB 0 117 44 0 STO 0
028 23 SIN 073 45 1 RCL 1 118 43 32 g RTN
029 45 2 RCL 2 074 45 3 RCL 3 119 42,21, 9 f LBL 9
030 45 6 RCL 6 075 43 10 g x≤y 120 24 COS
031 40 + 076 22 8 GTO 8 121 16 CHS
032 23 SIN 077 42,21, 7 f LBL 7 122 43 24 g COS⁻¹
033 10 ÷ 078 2 2 123 43 32 g RTN
034 45 1 RCL 1 079 32 15 GSB E 124 42,21, 8 f LBL 8
035 20 × 080 43 32 g RTN 125 1 1
036 44 3 STO 3 081 42,21,11 f LBL A 126 32 15 GSB E
037 22 0 GTO 0 082 45 6 RCL 6 127 43 32 g RTN
038 42,21, 3 f LBL 3 083 32 9 GSB 9 128 42,21,15 f LBL E
039 44 4 STO 4 084 44 6 STO 6 129 43, 4, 9 g SF 9
040 33 R⬇ 085 45 4 RCL 4 130 31 R/S
041 44 2 STO 2 086 40 + 131 43, 5, 9 g CF 9
042 33 R⬇ 087 32 9 GSB 9 132 43 32 g RTN
043 44 1 STO 1 088 44 2 STO 2
044 45 4 RCL 4 089 22 0 GTO 0