BrownMath.com →TI-83/84/89 →Solving Triangles
Replies to: SAT / SAT II Math Programs for Your Calculator #1. But before i even ask how to get to your instruction of programming them in. Are these possible on a ti-83 plus? And if they are. What do i press to get to the prompt A.B.
Copyright © 2015–2019 by Stan Brown
Summary:Six numbers — three sides and threeangles — determine a triangle. If you know any three ofthem, providing that at least one of the three is a side, you canfind the other three.This program does just that, and as a bonus itfinds the area of the triangle.(You can also get all three sides fromtwo angles and the area.)The program figures out whether you’re in degree orradian mode, and adjusts itself accordingly.The program doesn’t check for negative angles or two enteredangles adding to more than 180° or 2π, so don’t besilly, m’kay?
The program works on all TI-83 Plus models, and all TI-84models including the color models.
See also:For the computations, please seeSolving Triangles. For the program code, see TRIANGLE.pdfin the accompanying TRIANGLE.zip file.
Contents:- Running the Program
Getting the Program
There are three methods to get the programinto your calculator:
- If you have a TI-84,download TRIANGLE.zip(31 KB,updated 28 Dec 2016), and unzip it.Use the USB cable that came with your calculator, and the freeTI Connect CE softwarefrom Texas Instruments, to transferthe TRIANGLE.8XP program to your calculator.
- If a classmate has the program on her calculator(any model TI-83+/84+),she can transfer it to yours, provided you both have a USB portor you both have a round I/O port. Connect the appropriate cable toboth calculators, inserting each end firmly.On your calculator, press [
2nd
x,T,θ,n
makesLINK
][►
] [ENTER
]. Then on hers press[2nd
x,T,θ,n
makesLINK
] [3
], selectTRIANGLE,and finally press [►
] [ENTER
].If you get a prompt about a duplicate program, choose Overwrite. - Or, as a last resort, key in the program.See TRIANGLE.pdf and TRIANGLE_hints.htm in theTRIANGLE.zip file.
Running the Program
It’s customary to refer to the angles as A, B, and C,and the sides as a, b, and c, such that side a is opposite angle A,side b is opposite angle B, and side c is opposite angle C.
When you run the TRIANGLE program, it prompts you tosay which facts you know:
- Angle-side-angle, two angles and the side between them.
- Angle-angle-side, two angles and one of the sides notbetween them.
- Side-angle-side, two sides and the angle between them.
- Side-side-angle, two sides and one of the angles notbetween them. For some values, this case can have two solutions. Theprogram will prompt you when that happens.
- Side-side-side, all three sides known.
- Angle-angle-angle-area, all three angles plus the area known.
Each case has either one unique solution, or none. The exceptionis SSA, which could have zero, one, or two solutions depending on thenumbers. For about that, see Example 3 below, andSpecial Note: Side-Side-Anglein Trig without Tears.
Example 1. Three Sides Known
Given the three sides of the triangle(menu item 5), you can use theprogram to find thethree angles. Run the TRIANGLE program and select
5:SSS
. Enter the three sides, and the program gives youthe area, the three angles, and the three sides. The first angle isopposite the first side, the second angle opposite the second side, andthe third angle opposite the third side.Angles are always displayed in degrees, with one decimalplace on black-white screens, two decimal places on color screens.If one of the angles is ≥100°, the b&wdisplay may be too narrow. In that case, just press [
ALPHA
MATH
makesA
],[ALPHA
APPS
makesB
], or [ALPHA
PRGM
makesC
] to display the angle. It’sthe unrounded value, so you can also do this to get full precision. Inthe screen shot at right, angle C is shown.In this case, of course you already know the sides. But incases where the program is computing them, you might want moreprecision than the program displays. Press [
ALPHA
x-1
makesD
],[ALPHA
SIN
makesE
], or [ALPHA
COS
makesF
] for sides a, b, c, or[ALPHA
TAN
makesG
] for the area.Example 2. Two Angles and Non-IncludedSide Known
When you know two angles and a side not between them,use
2:AAS
. Callthe known side a; then the angle opposite it is A and the anglebetween them is B. Here a = 180, A = 31°, and B =42°.The third angle is 107°. The base of the triangle is334.22; and the third side, opposite the 42° angle, is 233.85.
Example 3. Two Sides and Non-IncludedAngle Known
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please click to donate!Because this program helps you,
please donate at
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please click to donate!Because this program helps you,
please donate at
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Suppose you know that two sides measure 8 and 10 units. Youdon’t know the angle between them, but you know that the angleopposite the 8-unit side is 45°. There are actually two trianglesthat meet these conditions, a larger triangle with B as an acute angle(<90°), and a smaller triangle with B as an obtuse angle(>90°). Those triangles are also shown separately here, inbrown and blue respectively:
See Special Note:Side-Side-Angle for the exact conditions when SSA can give youzero, one, or two solutions.
Fortunately, the TRIANGLE programhas these conditions programmed in for you:select
4:SSA
.When there are twopossible solutions, the program prompts you to choose one. HereI’ve chosen the acute angle for B, which gives the largertriangle.And here I’ve chosen the obtuse angle for B, which givesthe smaller triangle.
Example 4. Area and Two Angles Known
If you know any two angles, you know the third one andtherefore you know the shape of thetriangle. Then, any one side or the area will let you solve the trianglecompletely.
Example: Suppose you know that a triangle has angles of30°, 50°, with area of 27.16. Make a sketch, using (spoileralert!) 100° for the third angle and about 12 units for the longside.
Solution: Select
6:AA and Area
, andwhen prompted enter the two angles and the area. (If you know allthree angles, it doesn’t matter which two you enter.)Remember that angle A is opposite side a, soside a = 6 units is opposite angle A = 30°, side b = 9.19 units is opposite angle B = 50°, and side c = 11.82 units is opposite angle C = 100°.
Program Variables
The TRIANGLE program uses several variables. They’relisted here because you might have occasion to use some of them afterthe program finishes:
- A, B, C are the entered and computed angles, in degrees.
- D, E, F are the entered and computed sides a, b, c.
- G is the area of the triangle, (ab/2) ×sin C.
- H is the height of the triangle, b × sin A.
- R is the total angles of the triangle, either180° or 2π radians.
- Z is 1 for color calculators and 0 for black-and-whitecalculators.
What’s New
- 26 Sept 2016: Update the “hints” file in the ZIPfile, with no change to the actual program.
- 4 Apr 2016: Program v1.2:
- The program now works in degree or radian mode.
- Add case 6, three angles and area known, assuggested in email by Caroline McKnoe. There’s aworked-out example in this article.
- Override the calculator’s “Done” prompt with'Press Enter…” to stop the heading for the answers fromscrolling off the top of the screen in Mathprint mode.
- 1 Jan 2016: Program v1.1:
- All TI-83+ and TI-84+ calculators are supported.Lower case is now used for readability, and todistinguish sides a, b, c from angles A, B, C.There’s special formatting for color screens.
- This article is new, with details that didn’t belong in thetextbook and several worked examples.
- 21 Sept 2002: Program v1.0, to accompany theTrig without Tears textbook.
Because this program helps you,
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
Updates and new info: https://BrownMath.com/ti83/
Site Map |Home Page| Contact
BrownMath.com →TI-83/84/89 →Solving Triangles
Copyright © 2015–2019 by Stan Brown
Summary:Six numbers — three sides and threeangles — determine a triangle. If you know any three ofthem, providing that at least one of the three is a side, you canfind the other three.This program does just that, and as a bonus itfinds the area of the triangle.(You can also get all three sides fromtwo angles and the area.)The program figures out whether you’re in degree orradian mode, and adjusts itself accordingly.The program doesn’t check for negative angles or two enteredangles adding to more than 180° or 2π, so don’t besilly, m’kay?
The program works on all TI-83 Plus models, and all TI-84models including the color models.
See also:For the computations, please seeSolving Triangles. For the program code, see TRIANGLE.pdfin the accompanying TRIANGLE.zip file.
Contents:- Running the Program
Getting the Program
There are three methods to get the programinto your calculator:
- If you have a TI-84,download TRIANGLE.zip(31 KB,updated 28 Dec 2016), and unzip it.Use the USB cable that came with your calculator, and the freeTI Connect CE softwarefrom Texas Instruments, to transferthe TRIANGLE.8XP program to your calculator.
- If a classmate has the program on her calculator(any model TI-83+/84+),she can transfer it to yours, provided you both have a USB portor you both have a round I/O port. Connect the appropriate cable toboth calculators, inserting each end firmly.On your calculator, press [
2nd
x,T,θ,n
makesLINK
][►
] [ENTER
]. Then on hers press[2nd
x,T,θ,n
makesLINK
] [3
], selectTRIANGLE,and finally press [►
] [ENTER
].If you get a prompt about a duplicate program, choose Overwrite. - Or, as a last resort, key in the program.See TRIANGLE.pdf and TRIANGLE_hints.htm in theTRIANGLE.zip file.
Running the Program
![Ti 84 programs games Ti 84 programs games](/uploads/1/2/5/8/125828277/367327276.jpg)
It’s customary to refer to the angles as A, B, and C,and the sides as a, b, and c, such that side a is opposite angle A,side b is opposite angle B, and side c is opposite angle C.
When you run the TRIANGLE program, it prompts you tosay which facts you know:
- Angle-side-angle, two angles and the side between them.
- Angle-angle-side, two angles and one of the sides notbetween them.
- Side-angle-side, two sides and the angle between them.
- Side-side-angle, two sides and one of the angles notbetween them. For some values, this case can have two solutions. Theprogram will prompt you when that happens.
- Side-side-side, all three sides known.
- Angle-angle-angle-area, all three angles plus the area known.
Each case has either one unique solution, or none. The exceptionis SSA, which could have zero, one, or two solutions depending on thenumbers. For about that, see Example 3 below, andSpecial Note: Side-Side-Anglein Trig without Tears.
Example 1. Three Sides Known
Given the three sides of the triangle(menu item 5), you can use theprogram to find thethree angles. Run the TRIANGLE program and select
5:SSS
. Enter the three sides, and the program gives youthe area, the three angles, and the three sides. The first angle isopposite the first side, the second angle opposite the second side, andthe third angle opposite the third side.Angles are always displayed in degrees, with one decimalplace on black-white screens, two decimal places on color screens.If one of the angles is ≥100°, the b&wdisplay may be too narrow. In that case, just press [
ALPHA
MATH
makesA
],[ALPHA
APPS
makesB
], or [ALPHA
PRGM
makesC
] to display the angle. It’sthe unrounded value, so you can also do this to get full precision. Inthe screen shot at right, angle C is shown.In this case, of course you already know the sides. But incases where the program is computing them, you might want moreprecision than the program displays. Press [
ALPHA
x-1
makesD
],[ALPHA
SIN
makesE
], or [ALPHA
COS
makesF
] for sides a, b, c, or[ALPHA
TAN
makesG
] for the area.Example 2. Two Angles and Non-IncludedSide Known
When you know two angles and a side not between them,use
2:AAS
. Callthe known side a; then the angle opposite it is A and the anglebetween them is B. Here a = 180, A = 31°, and B =42°.The third angle is 107°. The base of the triangle is334.22; and the third side, opposite the 42° angle, is 233.85.
Example 3. Two Sides and Non-IncludedAngle Known
Because this program helps you,
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
Suppose you know that two sides measure 8 and 10 units. Youdon’t know the angle between them, but you know that the angleopposite the 8-unit side is 45°. There are actually two trianglesthat meet these conditions, a larger triangle with B as an acute angle(<90°), and a smaller triangle with B as an obtuse angle(>90°). Those triangles are also shown separately here, inbrown and blue respectively:
See Special Note:Side-Side-Angle for the exact conditions when SSA can give youzero, one, or two solutions.
Fortunately, the TRIANGLE programhas these conditions programmed in for you:select
4:SSA
.When there are twopossible solutions, the program prompts you to choose one. HereI’ve chosen the acute angle for B, which gives the largertriangle.And here I’ve chosen the obtuse angle for B, which givesthe smaller triangle.
Example 4. Area and Two Angles Known
If you know any two angles, you know the third one andtherefore you know the shape of thetriangle. Then, any one side or the area will let you solve the trianglecompletely.
Example: Suppose you know that a triangle has angles of30°, 50°, with area of 27.16. Make a sketch, using (spoileralert!) 100° for the third angle and about 12 units for the longside.
Solution: Select
6:AA and Area
, andwhen prompted enter the two angles and the area. (If you know allthree angles, it doesn’t matter which two you enter.)Remember that angle A is opposite side a, soside a = 6 units is opposite angle A = 30°, side b = 9.19 units is opposite angle B = 50°, and side c = 11.82 units is opposite angle C = 100°.
Program Variables
The TRIANGLE program uses several variables. They’relisted here because you might have occasion to use some of them afterthe program finishes:
- A, B, C are the entered and computed angles, in degrees.
- D, E, F are the entered and computed sides a, b, c.
- G is the area of the triangle, (ab/2) ×sin C.
- H is the height of the triangle, b × sin A.
- R is the total angles of the triangle, either180° or 2π radians.
- Z is 1 for color calculators and 0 for black-and-whitecalculators.
What’s New
- 26 Sept 2016: Update the “hints” file in the ZIPfile, with no change to the actual program.
- 4 Apr 2016: Program v1.2:
- The program now works in degree or radian mode.
- Add case 6, three angles and area known, assuggested in email by Caroline McKnoe. There’s aworked-out example in this article.
- Override the calculator’s “Done” prompt with'Press Enter…” to stop the heading for the answers fromscrolling off the top of the screen in Mathprint mode.
- 1 Jan 2016: Program v1.1:
- All TI-83+ and TI-84+ calculators are supported.Lower case is now used for readability, and todistinguish sides a, b, c from angles A, B, C.There’s special formatting for color screens.
- This article is new, with details that didn’t belong in thetextbook and several worked examples.
- 21 Sept 2002: Program v1.0, to accompany theTrig without Tears textbook.
Because this program helps you,
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
please click to donate!Because this program helps you,
please donate at
BrownMath.com/donate.
Updates and new info: https://BrownMath.com/ti83/
Site Map |Home Page| Contact