Right Triangle: c2 = a2 + b2 45-45-90
Acute Triangle: c2 < a2 + b2
Obtuse Triangle: c2 > a2 + b2
30-60-90
Pythagorean Converse
c2 a2 + b2
Special Right Triangles
Angles of
Elevation &
Depression
Sin Θ = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑒𝑢𝑠𝑒 Cos Θ =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑒𝑢𝑠𝑒 Tan Θ =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Sin A =
Cos A =
Tan A =
Sin B =
Cos B =
Tan B =
Sin C =
Cos C =
Tan C =
To find an angle, use Inverse Trig Functions: sin–1 cos–1 tan–1
Leg Rule
SOH CAH TOA
Altitude Rule
Right Triangles: Formulas and Properties
Graphic Organizer/ Reference (p.1)
Pythagorean Theorem
hypotenusetheisc
legsareb&a
;cba222
Converse of the
Pythagorean Theorem
;cba:obtuse
;cba:right
;cba:acute
222
222
222
Pythagorean Triple
A set of three whole numbers that solve the
Pythagorean Theorem. (3-4-5 is the most common.)
A
B C
c b
a
45-45-90 A
B C n
n2n
30-60-90 A
C B
n2
n
3n30
o
60o
45o
45o
Right Triangles: Formulas and Properties
Graphic Organizer/ Reference (p. 2)
Trigonometry
AB
ACBsin
AB
BCAsin
hypotenuse
oppositesine
A
B C
c b
a
Law of Sines
A
B C
AB
BCBcos
AB
ACAcos
hypotenuse
adjacentcosine
BC
ACBtan
AC
BCAtan
adjacent
oppositeangentt
c
Csin
b
Bsin
a
Asin
c b
a
Law of Cosines
Ccosabbac
Bcosaccab
Acosbccba
2
2
2
222
222
222
A
B C
c b
a
© ("Secondary Math Shop) 2013
SOH – CAH – TOA
S – Sine
O – Opposite
H – Hypotenuse
hyp
oppsin
C – Cosine
A – Adjacent
H – Hypotenuse
T – Tangent
O – Opposite
A – Adjacent
side opp B
side adj A
side opp A
side adj B
hypotenuse
A
C B
***Reminder***
Hypotenuse: the side opposite the right angle
Adjacent: the side “attached” to the acute angle that is NOT the hypotenuse
Opposite: the side that does not form the acute angle
© ("Secondary Math Shop) 2013
We are given the angle, the opposite
and the hypotenuse so that this is a
sine problem.
calculatorinputx
bysidesbothmultiplyx
ratiotrigupsetx
7.4
836sin8
836sin
We are given the angle, the adjacent and
the hypotenuse so that this is a cosine
problem.
calculatorinputx
anglethefindtoinversethetakex
ratiotrigupsetx
2.48
cos)6
4(cos
6
4cos
1
We are given the angle, the opposite
and the adjacent so that this is a
tangent problem.
calculatorinputx
bysidesbothmultiplyx
ratiotrigupsetx
0.6
550tan5
550tan
We are given the angle, the opposite
and the hypotenuse so that this is a
sine problem.
calculatorinputx
bysidesbothdividex
multiplycrossx
ratiotrigupsetx
7.7
70sin70sin
2.7
2.7)70(sin
2.770sin