The Museum of HP Calculators

# Triangle Solution a, b, c for the HP-55

This program is Copyright © 1975 by Hewlett-Packard and is used here by permission. This program was originally published in "HP-55 Mathematics Programs".

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

## Overview

Given three sides of a triangle this program solves the triangle for the remaining parameters by the following formulas:

C = cos-1((a2+b2-c2)/2ab)
B = sin-1(b*sin(C)/c)
A = sin-1(a*sin(C)/c)

Reletter if necessary to make c the largest side. The program works in any angular mode. However, if in degree mode decimal degrees are assumed.

## Instructions

 Step Instructions Input Data/Units Keys Output Data/Units 1 Enter program 2 Store a, b, and c (c is the largest) a STO 1 b STO 2 c STO 3 3 Find the solution BST R/S C* R/S B* R/S A * The stack must be maintained at these positions.

## Example

Given the following three sides:

a = 30.3
b = 40.4
c = 62.6

Solve the triangle.

Solution:
C= 123.99°
B = 32.35°
A= 23.66°

## The Program

```LINE CODE KEYS
00.
01.   34  RCL
02.   01  1
03.   41  ENTER
04.   71  x
05.   34  RCL
06.   02  2
07.   41  ENTER
08.   71  x
09.   61  +
10.   34  RCL
11.   03  3
12.   41  ENTER
13.   71  x
14.   51  -
15.   34  RCL
16.   01  1
17.   34  RCL
18.   02  2
19.   71  x
20.   02  2
21.   71  x
22.   81  ÷
23.   32  g
24.   13  cos-1
25.   84  R/S
26.   31  f
27.   12  sin
28.   34  RCL
29.   03  3
30.   81  ÷
31.   34  RCL
32.   02  2
33.   22  x<>y
34.   71  x
35.   31  f
36.   34  LAST X
37.   22  x<>y
38.   32  g
39.   12  sin-1
40.   84  R/S
41.   23  roll dn
42.   34  RCL
43.   01  1
44.   71  x
45.   32  g
46.   12  sin-1
47.  -00  GTO 00
```

```R1  a
R2  b
R3  c
```