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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 - PowerPoint PPT Presentation
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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 Triangles45°-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 Triangles30°-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.
