Unit 2 - Right Triangles and
Trigonometry
Chapter 8
Triangle Inequality Theorem


Need to know if a set of numbers can
actually form a triangle before you classify it.
Triangle Inequality Theorem: The sum of any
two sides must be larger than the third.
◦ Example: 5, 6, 7
 Since 5+6 > 7
it is a triangle
6+7 > 5
5+7 > 6
2+3 > 1
3+1 > 2
◦ Example: 1, 2, 3
 Since 1+2 = 3
it is not a triangle!
Examples - Converse

Can this form a
triangle?

Can this form a
triangle?

Prove it: Show the
work!

Prove it: Show the
Work!
Pythagorean Theorem and
Its Converse


Pythagorean Theorem
𝑎2 + 𝑏 2 = 𝑐 2

Converse of the
Pythagorean Theorem

c2 < a2 + b2 then Acute

c2 = a2 + b2 then Right

c2 > a2 + b2 then
Obtuse
c
a
b
Examples – What type of triangle
am I?
1.
.
3.
4.
2.
.
Pythagorean Triple


A set of nonzero
whole numbers a, b,
and c that satisfy the
equation 𝑎2 + 𝑏 2 =
𝑐2
Common Triples
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

They can also be
multiples of the
common triples such
as:
6, 8, 10
9, 12, 15
15, 20, 25
14, 28, 50
Section 8.2
SPECIAL RIGHT
TRIANGLES
Special Right Triangles
45°-45°-90°
𝑥 2
x
x
45° 45° 90°
x
x
𝑥 2
Examples – Solve for the Missing
Sides

Solve or x and y

Solve for e and f
Special Right Triangles
30°-60°-90°
30° 60° 90°
𝑥 3
2x
x
x
𝑥 3
2x
Examples – Solve for the Missing
Sides

Solve for x and y

Solve for x and y
Section 8.3
RIGHT TRIANGLE
TRIGONOMETRY
Trigonometric Ratios

Sine = Opposite
Hypotenuse

Cosine =

Tangent = Opposite
Adjacent
Adjacent
Hypotenuse
𝑂
 sin
𝐻
𝐴
cos
𝐻
𝑂
tan
𝐴
SOHCAHTOA
REMEMBER THIS!!!!
WRITE THIS ON THE TOP
OF YOUR PAPER ON ALL
TESTS AND HOMEWORK!
Set up the problem
Sin
 Cos
 Tan

Sin
 Cos
 Tan

Set up the problem
Sin
 Cos
 Tan

Trigonometric Ratios:

When you have the
angle you would use:
sin
 cos
 tan


When you need the
angle you would use:
sin−1
 cos −1
 tan−1

Examples

Solve for the missing
variable

Solve for the missing
variable
Examples

Solve for the missing
variable

Solve for the missing
variable
Examples

Find m< A and m< B
Examples

Solve for the missing
variables
Section 8.4
ANGLE OF ELEVATION
AND ANGLE OF
DEPRESSION
Elevation verse Depression –
Point of View

Angle of Elevation

Angle of Depression
Examples – Point of View

Elevation

Depression
Examples – Point of View

Find the Angle
Elevation

Find the Height of
the boat from the
sea floor.