Spherical Triangle Solver: Programmed on a TI84+ C Silver Edition
This could easily be ported to other programming calculators given how basic the TI84+ programming is.
Variables:
"Sides" (Subtending Angles): X, Y, Z
Corresponding Angles: A, B, C
I try to capture all possible traps. No guarantees by I try. This program is rather large, about 1,500 bytes. Ending quotes and parenthesis can be left out on the TI84+ but I present them in the text for completeness.
PROGRAM: SPHTRI
: Lbl 0
: ClrHome
: Output(1,1,"ANGLE (θ),SIDE")
: Output(2,1,"A, X")
: Output(3,1,"B, Y")
: Output(4,1,"C, Z")
: Output(6,1,"PRESS ENTER TO GO ON")
: Pause
: ClrHome
: Menu("KNOWN:","3 SIDES",1,
"2 S,INT θ (X,Y,C)",2,
"2 S,EXT θ (Y,Z,B)",3,
"1 S,2 ADJ θ (Z,A,B)",4,
"2 θS, ADJ SIDE (X,A,B)",5,
"3 ANGLES", 6
"EXIT",7)
: Lbl 1
: Input "SIDE X:", X
: Input "SIDE Y:", Y
: Input "SIDE Z:", Z
: If X+Y+Z>360°
: Then
: Disp "NO SOLN"
: Pause
: Goto 0
: End
: cos^1 (( cos(X)  cos(Y) cos(Z) )/( sin(Y) sin(Z) )→ A
: cos^1 (( cos(Y)  cos(X) cos(Z) )/( sin(X) sin(Z) )→ B
: cos^1 (( cos(Z)  cos(X) cos(Y) )/( sin(X) sin (Y) )→ C
: Disp "A,B,C:",A,B,C
: Pause
: Goto 0
: Lbl 2
: Input "SIDE X:", X
: Input "SIDE Y:", Y
: Input "θ BETWEEN C:", C
: cos^1 ( cos(X) cos(Y) + sin(X) sin(Y) cos(C) ) → Z
: sin^1 ( sin(C) sin(X) / sin(Z) ) → A
: sin^1 ( sin(C) sin(Y) / sin(Z) ) → B
: Disp "Z,A,B:",Z,A,B
: Pause
: Goto 0
: Lbl 3
: Input "SIDE Y:", Y
: Input "CORR. θ B:", B
: Input "ADJ. SIDE Z:", Z
: If Y < sin^1 (sin(Z) sin(B) )
: Then
: Disp "NO SOLN."
: Pause
: Goto 0
: End
: sin^1 ( sin(Z) sin(B) / sin(Y) ) → C
: 2 tan^1 ( tan(.5Y  .5Z) sin(.5B + .5C) / sin(.5B  .5C) ) → X
: 2 tan^1 ( sin(.5Y  .5Z) / tan(.5B  .5C) / sin(.5Y + .5Z) ) → A
: Disp "C,X,A:",C,X,A
: Pause
: If Y
: 180°  C → S
: 2 tan^1 (tan(.5Y  .5Z) sin(.5B + .5C) / sin(.5B  .5C) ) → T
: 2 tan^1 (sin(.5Y  .5Z) / tan(.5B  .5S) / sin(.5Y + .5Z) ) → U
: Disp "ALT C,X,A:",S,T,U
: Pause
: End
: Goto 0
: Lbl 4
: Input "θ A:", A
: Input "θ B:", B
: Input "SIDE BETWEEN Z:", Z
: cos^1 ( sin(A) sin(B) cos(Z)  cos(A) cos(B) ) → C
: cos^1 ( (cos(A) + cos(B) cos(C)) / (sin(B) sin(C)) → X
: cos^1 ( (cos(B) + cos(A) cos(C)) / (sin(A) sin(C)) → Y
: Disp "C,X,Y:",C,X,Y
: Pause
: Goto 0
: Lbl 5
: Input "θ A:", A
: Input "CORR. SIDE X:", X
: Input "ADJ θ B:", B
: sin^1 (sin(X) sin(B) / sin(A) ) → Y
: 2 tan^1 (tan(.5X.5Y) sin(.5A+.5B) / sin(.5A.5B)) → Z
: 2 tan^1 (sin(.5X.5Y) / tan(.5A.5B) / sin(.5X+.5Y)) → C
: Disp "Y,C,Z:", Y,C,Z
: Pause
: Goto 0
: Lbl 6
: Input "θ A:", A
: Input "θ B:", B
: Input "θ C:", C
: If A+B+C<180° or A+B+C>540°
: Then
: Disp "NO SOLN."
: Goto 0
: Pause
: End
: Prompt A,B,C
: cos^1 ((cos(A) + cos(B) cos(C))/(sin(B) sin(C)) → X
: cos^1 ((cos(B) + cos(A) cos(C))/(sin(A) sin(C))→ Y
: cos^1 ((cos(C) + cos(A) cos(B))/(sin(A) sin(B)) → Z
: Disp "X,Y,Z:",X,Y,Z
: Pause
: Goto 0
: Lbl 7
Sources:
Wikipedia: Solutions of Triangles
http://en.wikipedia.org/wiki/Solution_of_triangles#Solving_spherical_triangles
Had To Know: Spherical Trigonometry Calculator
http://www.had2know.com/academics/sphericaltrigonometrycalculator.html
Examples  in Degrees Mode:
1. Given 3 Sides:
X: 34.49°
Y: 28.11°
Z: 29.00°
Solutions:
A: 76.64274255°
B: 54.05239674°
C: 56.40782913°
2. Given 2 Side with Interior Angle
X: 5.58°
Y: 7.24°
C: 164°
Solutions:
Z: 12.69684035°
A: 7.004143971°
B: 9.093527785°
3. Given 2 Sides with Exterior (Adjacent) Angle:
Y: 14.41°
B: 77.97°
Z: 18.00°
No Solution
Y: 7.09°
B: 44.8°
Z: 6.36°
Solutions:
C: 39.22735167°
X: 10.02551866°
A: 96.36477875°
4. Given 1 side and 2 adjacent angles
A: 75°
B: 88°
Z: 4.53°
Solutions:
C: 17.58132838°
X: 14.62939892°
Y: 15.14817154°
5. Given 2 Angles and 1 adjacent side
A: 103°
X: 2.66°
B: 71°
Solutions:
Y: 2.581182188°
C: 6.006268443°
Z: .2855550692°
6. Given 3 interior angles
A: 89°
B: 66°
C: 70°
Solutions:
X: 79.49157643°
Y: 63.94337829°
Z: 67.52897419°
This blog is property of Edward Shore. 2013
A blog is that is all about mathematics and calculators, two of my passions in life.
Friday, July 5, 2013
Spherical Triangle Solver  TI84+
Subscribe to:
Post Comments (Atom)
HP 15C: Pythagorean Triples
HP 15C: Pythagorean Triples This program calculates the Pythagorean triple (A, B, C) such that A^2 + B^2 = C^2 by the formulas: ...

TI36X Pro Review This is a review of the TI36X Pro Calculator by Texas Instruments. History Originally, this was the TI30X Pro that w...

Casio fx991EX Classwiz Review Casio FX991EX The next incarnation of the fx991 line of Casio calculators is the fx991 EX. ...

One of the missing features of the TI82/83/84 family is the ability to convert between bases. Here are two programs in TIBasic to help...
No comments:
Post a Comment