law of cosines
Generalized Pythagorean theorem
The law of cosines is a formula relating the lengths of a triangle's sides to the cosine of one of its angles.
It generalizes the Pythagorean theorem to non-right triangles: for any triangle with sides a, b, and c, where C is the angle opposite side c, the relationship is c² = a² + b² − 2ab cos(C).
The formula allows calculating an unknown side when two sides and the included angle are known, or finding angles when all three sides are known.
All sides unequal
- isoscelesTwo sides match
- equilateralHaving all sides congruent
- acuteIntensely severe or perceptive
- obtuseLacking mental sharpness
sides · vertices · angle measurement · SAS · SSS · congruence · similarity · Pythagorean theorem
Sum of component products
- displacementRemoval from usual location
- resultantCombined effect of factors
- projectionSomething that extends outward
Mathematical equality assertion
- derivationSource or origin tracing
- proofDemonstration of truth
- theoremDemonstrated logical conclusion
- calculationMathematical problem-solving process
substitution · algebraic manipulation · quadratic · square root · simplification · rearrangement · solving · generalization
Measuring and charting terrain
- navigationDetermining position and course
- triangulationLocation via three points
- GPSSatellite-based location technology
- astronomyScience of celestial objects
physics · engineering · cartography · land measurement · satellite positioning · flight paths · structural analysis · ballistics
Opposite over hypotenuse
- tangentLine touching curve once
- arccosInverse of cosine
- trigonometric functionsRatios relating angles to sides
- unit circleRadius-one circle at origin
radians · degrees · inverse functions · secant · cosecant · cotangent
scalene
All sides unequal
- isoscelesTwo sides match
- equilateralHaving all sides congruent
- acuteIntensely severe or perceptive
obtuse · sides · vertices · angle measurement · SAS · SSS · congruence · similarity · Pythagorean theorem · law of sines
dot product
Sum of component products
- displacementRemoval from usual location
- resultantCombined effect of factors
- projectionSomething that extends outward
equation
Mathematical equality assertion
- derivationSource or origin tracing
- proofDemonstration of truth
- theoremDemonstrated logical conclusion
calculation · substitution · algebraic manipulation · quadratic · square root · simplification · rearrangement · solving · generalization
surveying
Measuring and charting terrain
- navigationDetermining position and course
- triangulationLocation via three points
- GPSSatellite-based location technology
astronomy · physics · engineering · cartography · land measurement · satellite positioning · flight paths · structural analysis · ballistics · geodesy
sine
Opposite over hypotenuse
- tangentLine touching curve once
- arccosInverse of cosine
- trigonometric functionsRatios relating angles to sides
unit circle · radians · degrees · inverse functions · secant · cosecant · cotangent
- trigonometrysine, tangent, secant, cosecant, cotangent
- geometry formulasPythagorean theorem, area, perimeter, circumference, surface area
- Math RulesPythagorean theorem, distributive property, commutative property, associative property, order of operations
- precalculusfunctions, polynomials, trigonometry, logarithms, exponential functions
- trig identities
- math termsnumbers, plus or minus, linear growth, square, operand