law of sines
Angle-side ratio rule
The law of sines is a formula relating the sides of a triangle to the sines of their opposite angles: each side divided by the sine of its opposite angle equals the same constant.
It allows solving triangles when you know some combination of sides and angles but not all: Using the law of sines, we found the missing angle was 47 degrees.
Facing or contrary position
- scaleneAll sides unequal
- isoscelesTwo sides match
- acute trianglePolygon with three sub-90° corners
- obtuse triangleTriangle with angle over ninety
ASA · SSA · vertex · sides · angles · altitude · circumradius · area formula
Comparative numerical relation
- proportionComparative relation of parts
- cross-multiplicationMethod for solving proportions
- substitutionExchange of one for another
- rearrangementAltered ordering of elements
derivation · proof · equation · sin · arcsin · calculation · algebraic manipulation · approximation
Measuring and charting terrain
- navigationDetermining position and course
- triangulationLocation via three points
- distance measurementQuantifying spatial intervals
- angle of elevationMeasure of upward tilt
astronomy · cartography · engineering · architecture · physics · bearing
opposite side
Facing or contrary position
- scaleneAll sides unequal
- isoscelesTwo sides match
- acute trianglePolygon with three sub-90° corners
obtuse triangle · ASA · SSA · vertex · sides · angles · altitude · circumradius · area formula · proportionality
ratio
Comparative numerical relation
- proportionComparative relation of parts
- cross-multiplicationMethod for solving proportions
- substitutionExchange of one for another
rearrangement · derivation · proof · equation · sin · arcsin · calculation · algebraic manipulation · approximation
surveying
Measuring and charting terrain
- navigationDetermining position and course
- triangulationLocation via three points
- distance measurementQuantifying spatial intervals
angle of elevation · astronomy · cartography · engineering · architecture · physics · bearing
Pythagorean theorem
Relates right triangle sides
- area formulaExpression for calculating space
- trigonometrysecant, cosecant, cotangent, sin, cos
- Formulaschemical formula, quadratic formula, empirical formula, area formula, volume formula
- geometry formulasPythagorean theorem, area, perimeter, circumference, surface area
- precalculusfunctions, polynomials, trigonometry, logarithms, exponential functions
- trig identities
- math termsnumbers, plus or minus, linear growth, square, operand
law, laws, law of cosines, tangent, sine, cosine, sinusoid, sinusoidal, sines