This document discusses the trigonometric relationships SOH CAH TOA, which are used to find unknown sides of a right triangle based on a known side and the trigonometric function (sine, cosine, or tangent) of one of the angles. It explains that sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. The document provides an example of using SOH CAH TOA to solve for an unknown side of a right triangle given one of the angle measures and a known side. It recommends memorizing and using SOH CAH TOA whenever working with right triangles in trigonometry.

1. Trigonometry SOH CAHTrigonometry SOH CAH
TOATOA
By William ColemanBy William Coleman
October 26October 26thth
20102010

2. IntroIntro
 SOH,CAH,TOA Is A Branch OfSOH,CAH,TOA Is A Branch Of
Mathematic Skills Used To Find TheMathematic Skills Used To Find The
Opposite Over The Hypotenuse.Opposite Over The Hypotenuse.
SS
OO
HH
SSine =ine = OOpposite overpposite over
HHypotenuse.ypotenuse.
CC
AA
HH
CCosine =osine = AAdjacent overdjacent over
HHypotenuse.ypotenuse.
TT
OO
AA
TTangent =angent = OOpposite overpposite over
AAdjacent.djacent.

3. How To Solve The Unknowns Of A 90How To Solve The Unknowns Of A 90
Degree TriangleDegree Triangle
 1. Make The Unknown Side The Numerator Of A1. Make The Unknown Side The Numerator Of A
Fraction, And Make TheFraction, And Make The KnownKnown Side The Denominator.Side The Denominator.
UnknownUnknown
Known =a/10Known =a/10

2. Name That Function Of The Angle Unknown2. Name That Function Of The Angle Unknown
Known =Known = a/10=sin 36 Degrees a/10=sin 36 Degrees
 3.Use The Trigonometric Table To Evaluate That3.Use The Trigonometric Table To Evaluate That
Function. Unknown Known =Function. Unknown Known = a/ a/10 = sin 36° = .58810 = sin 36° = .588
 4. Solve For The Unknown Side.4. Solve For The Unknown Side.aa = 10 ×= 10 × ..588 cm =588 cm =
55..88 cm88 cm

4. SOHSOH
 S=SinS=Sin
 O=OppositeO=Opposite
 H=HypotenuseH=Hypotenuse
sinesine of an angle is the ratio of the length ofof an angle is the ratio of the length of
the opposite side to the length of thethe opposite side to the length of the
hypotenuse Thehypotenuse The tangenttangent of an angle isof an angle is
the ratio of the length of the opposite sidethe ratio of the length of the opposite side
to the length of the adjacent side. In ourto the length of the adjacent side. In our
casecase

5. CAHCAH
 CosineTheCosineThe tangenttangent of an angle is the ratioof an angle is the ratio
of the length of the opposite side to theof the length of the opposite side to the
length of the adjacent side. In our caselength of the adjacent side. In our case
 AdjacentAdjacent
 HypotenuseHypotenuse
 TheThe cosinecosine of an angle is the ratio of theof an angle is the ratio of the
length of the adjacent side to the length oflength of the adjacent side to the length of
the hypotenusethe hypotenuse

6. TOATOA
 TangentTangent
 OppositeOpposite
 AdjacentAdjacent
 TheThe tangenttangent of an angle is the ratioof an angle is the ratio
of the length of the opposite side toof the length of the opposite side to
the length of the adjacent side. Inthe length of the adjacent side. In
our caseour case

7. SummarySummary
 As You Can See The SOH CAH TOA IsAs You Can See The SOH CAH TOA Is
A Very Helpful Tool When It ComesA Very Helpful Tool When It Comes
To Find The Sin Cosine And TangentTo Find The Sin Cosine And Tangent
Of A Triangle And Would RecommendOf A Triangle And Would Recommend
Using It Every Time You Are Stuck InUsing It Every Time You Are Stuck In
Trigonometry After You Learn HowTrigonometry After You Learn How
TO Use It.TO Use It.