DuckieDai Law of Cosines Python Program

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geometry · MIT License

Overview

Solve any side or angle of a triangle with the law of cosines and validate triangle inputs.

Usage

Inputs

Requested side or angle
Two sides and included angle, or all three positive side lengths

Outputs

Requested side or angle in degrees

Units: Use one consistent length unit; angles are degrees.

Assumptions and limitations

Assumptions

Supplied values describe one nondegenerate triangle.

Constraints

Sides are positive; angles are strictly between 0 and 180 degrees.

Known failures

Invalid triangle side sets are identified.
Inconsistent length units produce an incorrect result.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact source owner-tested through TI Connect CE
What happened: Owner confirmed the supplied law of cosines program runs on the physical calculator.
Dependencies: math
Suggested calculator name: COSLAW — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

Try the side-c calculation

This browser preview calculates side c from sides a and b and included angle C in degrees. The TI program also solves the other sides and all angles.

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Exact reviewed bytes

Source code

Download .py

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"""DuckieDai Law of Cosines for TI-84 Plus CE Python."""

from math import sqrt, cos, acos, radians, degrees


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def positive_number(prompt):
    """Require a positive number."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def angle_number(prompt):
    """Require an angle between 0 and 180 degrees."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 180:
                return value

        except ValueError:
            pass

        print("Angle must be")
        print("between 0 and 180.")


def valid_triangle(a, b, c):
    """Check triangle inequality."""
    return (
        a + b > c and
        a + c > b and
        b + c > a
    )


def safe_acos(value):
    """Protect against tiny rounding errors."""
    if value > 1:
        value = 1

    if value < -1:
        value = -1

    return acos(value)


def show_answer(name, value, unit):
    print()
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("LAW OF COSINES")

    print("LAW OF COSINES")
    print()
    print("c^2 = a^2 + b^2")
    print("      -2ab*cos(C)")
    print()
    print("What do you need?")
    print()
    print("1. Side a")
    print("2. Side b")
    print("3. Side c")
    print("4. Angle A")
    print("5. Angle B")
    print("6. Angle C")
    print()

    choice = input("Choose 1-6: ")

    print()

    # ==========================================
    # 1. SOLVE SIDE a
    #
    # a^2 = b^2 + c^2 - 2bc*cos(A)
    # ==========================================

    if choice == "1":

        b = positive_number("Side b: ")
        c = positive_number("Side c: ")
        A = angle_number("Angle A (deg): ")

        value = (
            b ** 2 +
            c ** 2 -
            2 * b * c * cos(radians(A))
        )

        if value <= 0:
            print("No valid triangle.")

        else:
            a = sqrt(value)

            print()
            print("Using:")
            print("a^2=b^2+c^2")
            print("   -2bc*cos(A)")

            show_answer(
                "a",
                a,
                "units"
            )

    # ==========================================
    # 2. SOLVE SIDE b
    #
    # b^2 = a^2 + c^2 - 2ac*cos(B)
    # ==========================================

    elif choice == "2":

        a = positive_number("Side a: ")
        c = positive_number("Side c: ")
        B = angle_number("Angle B (deg): ")

        value = (
            a ** 2 +
            c ** 2 -
            2 * a * c * cos(radians(B))
        )

        if value <= 0:
            print("No valid triangle.")

        else:
            b = sqrt(value)

            print()
            print("Using:")
            print("b^2=a^2+c^2")
            print("   -2ac*cos(B)")

            show_answer(
                "b",
                b,
                "units"
            )

    # ==========================================
    # 3. SOLVE SIDE c
    #
    # c^2 = a^2 + b^2 - 2ab*cos(C)
    # ==========================================

    elif choice == "3":

        a = positive_number("Side a: ")
        b = positive_number("Side b: ")
        C = angle_number("Angle C (deg): ")

        value = (
            a ** 2 +
            b ** 2 -
            2 * a * b * cos(radians(C))
        )

        if value <= 0:
            print("No valid triangle.")

        else:
            c = sqrt(value)

            print()
            print("Using:")
            print("c^2=a^2+b^2")
            print("   -2ab*cos(C)")

            show_answer(
                "c",
                c,
                "units"
            )

    # ==========================================
    # ANGLES REQUIRE ALL 3 SIDES
    # ==========================================

    elif choice == "4" or \
         choice == "5" or \
         choice == "6":

        a = positive_number("Side a: ")
        b = positive_number("Side b: ")
        c = positive_number("Side c: ")

        if not valid_triangle(a, b, c):

            print()
            print("INVALID TRIANGLE")
            print()
            print("These sides cannot")
            print("form a triangle.")

        # ======================================
        # 4. SOLVE ANGLE A
        #
        # cos(A) =
        # (b^2+c^2-a^2)/(2bc)
        # ======================================

        elif choice == "4":

            value = (
                b ** 2 +
                c ** 2 -
                a ** 2
            ) / (2 * b * c)

            A = degrees(
                safe_acos(value)
            )

            print()
            print("Using:")
            print("cos(A)=")
            print("(b^2+c^2-a^2)")
            print("/(2bc)")

            show_answer(
                "A",
                A,
                "degrees"
            )

        # ======================================
        # 5. SOLVE ANGLE B
        # ======================================

        elif choice == "5":

            value = (
                a ** 2 +
                c ** 2 -
                b ** 2
            ) / (2 * a * c)

            B = degrees(
                safe_acos(value)
            )

            print()
            print("Using:")
            print("cos(B)=")
            print("(a^2+c^2-b^2)")
            print("/(2ac)")

            show_answer(
                "B",
                B,
                "degrees"
            )

        # ======================================
        # 6. SOLVE ANGLE C
        # ======================================

        else:

            value = (
                a ** 2 +
                b ** 2 -
                c ** 2
            ) / (2 * a * b)

            C = degrees(
                safe_acos(value)
            )

            print()
            print("Using:")
            print("cos(C)=")
            print("(a^2+b^2-c^2)")
            print("/(2ab)")

            show_answer(
                "C",
                C,
                "degrees"
            )

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Law of Cosines for TI-84 Plus CE Python."""
from math import sqrt, cos, acos, radians, degrees
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def positive_number(prompt):
"""Require a positive number."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def angle_number(prompt):
"""Require an angle between 0 and 180 degrees."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 180:
return value
except ValueError:
pass
print("Angle must be")
print("between 0 and 180.")
def valid_triangle(a, b, c):
"""Check triangle inequality."""
return (
a + b > c and
a + c > b and
b + c > a
)
def safe_acos(value):
"""Protect against tiny rounding errors."""
if value > 1:
value = 1
if value < -1:
value = -1
return acos(value)
def show_answer(name, value, unit):
print()
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("LAW OF COSINES")
print("LAW OF COSINES")
print()
print("c^2 = a^2 + b^2")
print(" -2ab*cos(C)")
print()
print("What do you need?")
print()
print("1. Side a")
print("2. Side b")
print("3. Side c")
print("4. Angle A")
print("5. Angle B")
print("6. Angle C")
print()
choice = input("Choose 1-6: ")
print()
# ==========================================
# 1. SOLVE SIDE a
#
# a^2 = b^2 + c^2 - 2bc*cos(A)
# ==========================================
if choice == "1":
b = positive_number("Side b: ")
c = positive_number("Side c: ")
A = angle_number("Angle A (deg): ")
value = (
b ** 2 +
c ** 2 -
2 * b * c * cos(radians(A))
)
if value <= 0:
print("No valid triangle.")
else:
a = sqrt(value)
print()
print("Using:")
print("a^2=b^2+c^2")
print(" -2bc*cos(A)")
show_answer(
"a",
a,
"units"
)
# ==========================================
# 2. SOLVE SIDE b
#
# b^2 = a^2 + c^2 - 2ac*cos(B)
# ==========================================
elif choice == "2":
a = positive_number("Side a: ")
c = positive_number("Side c: ")
B = angle_number("Angle B (deg): ")
value = (
a ** 2 +
c ** 2 -
2 * a * c * cos(radians(B))
)
if value <= 0:
print("No valid triangle.")
else:
b = sqrt(value)
print()
print("Using:")
print("b^2=a^2+c^2")
print(" -2ac*cos(B)")
show_answer(
"b",
b,
"units"
)
# ==========================================
# 3. SOLVE SIDE c
#
# c^2 = a^2 + b^2 - 2ab*cos(C)
# ==========================================
elif choice == "3":
a = positive_number("Side a: ")
b = positive_number("Side b: ")
C = angle_number("Angle C (deg): ")
value = (
a ** 2 +
b ** 2 -
2 * a * b * cos(radians(C))
)
if value <= 0:
print("No valid triangle.")
else:
c = sqrt(value)
print()
print("Using:")
print("c^2=a^2+b^2")
print(" -2ab*cos(C)")
show_answer(
"c",
c,
"units"
)
# ==========================================
# ANGLES REQUIRE ALL 3 SIDES
# ==========================================
elif choice == "4" or \
choice == "5" or \
choice == "6":
a = positive_number("Side a: ")
b = positive_number("Side b: ")
c = positive_number("Side c: ")
if not valid_triangle(a, b, c):
print()
print("INVALID TRIANGLE")
print()
print("These sides cannot")
print("form a triangle.")
# ======================================
# 4. SOLVE ANGLE A
#
# cos(A) =
# (b^2+c^2-a^2)/(2bc)
# ======================================
elif choice == "4":
value = (
b ** 2 +
c ** 2 -
a ** 2
) / (2 * b * c)
A = degrees(
safe_acos(value)
)
print()
print("Using:")
print("cos(A)=")
print("(b^2+c^2-a^2)")
print("/(2bc)")
show_answer(
"A",
A,
"degrees"
)
# ======================================
# 5. SOLVE ANGLE B
# ======================================
elif choice == "5":
value = (
a ** 2 +
c ** 2 -
b ** 2
) / (2 * a * c)
B = degrees(
safe_acos(value)
)
print()
print("Using:")
print("cos(B)=")
print("(a^2+c^2-b^2)")
print("/(2ac)")
show_answer(
"B",
B,
"degrees"
)
# ======================================
# 6. SOLVE ANGLE C
# ======================================
else:
value = (
a ** 2 +
b ** 2 -
c ** 2
) / (2 * a * b)
C = degrees(
safe_acos(value)
)
print()
print("Using:")
print("cos(C)=")
print("(a^2+b^2-c^2)")
print("/(2ab)")
show_answer(
"C",
C,
"degrees"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: COSLAW.py
Size: 7413 bytes
SHA-256: 7dfce30271f47a7e54da6d412b332da2c91fe0a3695c6a6482257b3aedb045a6

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Version history

1.0.0 — current version, published 2026-09-24. Download this reviewed version

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