Spherical Triangle Solver: Programmed on a TI-84+ C Silver Edition

This could easily be ported to other programming calculators given how basic the TI-84+ 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 TI-84+ 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/spherical-trigonometry-calculator.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.

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