GMY-04

Law of cosines

Any angle.

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Geometrycosine law

Governing equation

c^2=a^2+b^2-2ab\\cos C

where

a: a (—)
b: b (—)
C: C (°)
c: c (—)

Lecture brief

Historical brief

Pythagoras, Heron, spherical trigonometry and the sphere’s volume are the measuring arts that predate calculus. The sheets compute length, area and angle on plane and sphere. This sheet (GMY-04 — Law of cosines) is the form associated with cosine law. Working symbols: $a$ , $b$ , $C$ $\rightarrow$ $c$ . Any angle.

Purpose

Purpose: compute

c

from

a

b

C

in Geometry via

c^2=a^2+b^2-2ab\\cos C

Any angle. Use it when a real geometry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 5.000\,\mathrm{—}

b = 7.000\,\mathrm{—}

C = 60.000\,\mathrm{^{\circ}}

, the governing relation

c^2=a^2+b^2-2ab\\cos C

yields

c = 6.2450\,\mathrm{—}

. Any angle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

a a5 —b b7 —C C60 °

Outputs

c c6.2450 —

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Narration of this film

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