Unit 2 - Right Triangles and TrigonometryChapter 8

Triangle Inequality TheoremNeed 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 6+7 > 5 5+7 > 6 it is a triangle

◦Example: 1, 2, 3 Since 1+2 = 3 2+3 > 1

3+1 > 2 it is not a triangle!

Examples - ConverseCan this form a

triangle?

Prove it: Show the work!

Can this form a triangle?

Prove it: Show the Work!

Pythagorean Theorem and Its ConversePythagorean

Theorem

c a

b

Converse of the Pythagorean Theorem

c2 < a2 + b2 then Acute

c2 = a2 + b2 then Right

c2 > a2 + b2 then Obtuse

Examples – What type of triangle am I?

1. .

2. .

3.

4.

Pythagorean TripleA set of nonzero

whole numbers a, b, and c that satisfy the equation

Common Triples3, 4, 55, 12, 138, 15, 177, 24, 25

They can also be multiples of the common triples such as:6, 8, 109, 12, 1515, 20, 2514, 28, 50

SPECIAL RIGHT TRIANGLES

Section 8.2

Special Right Triangles

45°-45°-90°

x

x

45° 45° 90°

x x

Examples – Solve for the Missing SidesSolve or x and y Solve for e and f

Special Right Triangles

30°-60°-90°

2x

x

30° 60° 90°

x 2x

Examples – Solve for the Missing SidesSolve for x and y Solve for x and y

RIGHT TRIANGLE TRIGONOMETRY

Section 8.3

Trigonometric RatiosSine = Opposite Hypotenuse

Cosine = Adjacent Hypotenuse

Tangent = Opposite Adjacent

SOHCAHTOA

REMEMBER THIS!!!!

WRITE THIS ON THE TOP OF YOUR PAPER ON ALL TESTS AND HOMEWORK!

Set up the problemSin CosTan

SinCosTan

Set up the problemSin CosTan

Trigonometric Ratios:

When you have the angle you would use:

When you need the angle you would use:

ExamplesSolve for the

missing variableSolve for the

missing variable

ExamplesSolve for the

missing variableSolve for the

missing variable

ExamplesFind m< A and m< B

ExamplesSolve for the

missing variables

ANGLE OF ELEVATION AND ANGLE OF DEPRESSION

Section 8.4

Elevation verse Depression – Point of ViewAngle of

ElevationAngle of

Depression

Examples – Point of ViewElevation Depression

Examples – Point of ViewFind the Angle

ElevationFind the Height

of the boat from the sea floor.