unit 2 - right triangles and trigonometry chapter 8
TRANSCRIPT
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Unit 2 - Right Triangles and TrigonometryChapter 8
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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!
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Examples - ConverseCan this form a
triangle?
Prove it: Show the work!
Can this form a triangle?
Prove it: Show the Work!
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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
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Examples – What type of triangle am I?
1. .
2. .
3.
4.
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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
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SPECIAL RIGHT TRIANGLES
Section 8.2
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Special Right Triangles
45°-45°-90°
x
x
45° 45° 90°
x x
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Examples – Solve for the Missing SidesSolve or x and y Solve for e and f
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Special Right Triangles
30°-60°-90°
2x
x
30° 60° 90°
x 2x
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Examples – Solve for the Missing SidesSolve for x and y Solve for x and y
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RIGHT TRIANGLE TRIGONOMETRY
Section 8.3
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Trigonometric RatiosSine = Opposite Hypotenuse
Cosine = Adjacent Hypotenuse
Tangent = Opposite Adjacent
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SOHCAHTOA
REMEMBER THIS!!!!
WRITE THIS ON THE TOP OF YOUR PAPER ON ALL TESTS AND HOMEWORK!
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Set up the problemSin CosTan
SinCosTan
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Set up the problemSin CosTan
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Trigonometric Ratios:
When you have the angle you would use:
When you need the angle you would use:
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ExamplesSolve for the
missing variableSolve for the
missing variable
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ExamplesSolve for the
missing variableSolve for the
missing variable
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ExamplesFind m< A and m< B
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ExamplesSolve for the
missing variables
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ANGLE OF ELEVATION AND ANGLE OF DEPRESSION
Section 8.4
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Elevation verse Depression – Point of ViewAngle of
ElevationAngle of
Depression
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Examples – Point of ViewElevation Depression
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Examples – Point of ViewFind the Angle
ElevationFind the Height
of the boat from the sea floor.