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Unit 2 - Right Triangles and Trigonometry Chapter 8

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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 > 76+7 > 5 5+7 > 6 it is a triangle ◦ Example: 1, 2, 3 Since 1+2 = 32+3 > 13+1 > 2 it is not a triangle!

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Examples - Converse Can 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 Converse Converse of the Pythagorean Theorem c 2 < a 2 + b 2 then Acute c 2 = a 2 + b 2 then Right c 2 > a 2 + b 2 then Obtuse

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Examples – What type of triangle am I? 1.. 2.. 3. 4.

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Pythagorean Triple They can also be multiples of the common triples such as: 6, 8, 10 9, 12, 15 15, 20, 25 14, 28, 50

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SPECIAL RIGHT TRIANGLES Section 8.2

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Special Right Triangles 45° 90° xx

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

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Special Right Triangles 30°60°90° x2x

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

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RIGHT TRIANGLE TRIGONOMETRY Section 8.3

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Trigonometric Ratios Sine = 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 problem Sin Cos Tan Sin Cos Tan

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Set up the problem Sin Cos Tan

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Trigonometric Ratios:

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Examples Solve for the missing variable

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Examples

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Examples Find m< A and m< B

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Examples Solve 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 View Angle of Elevation Angle of Depression

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Examples – Point of View Elevation Depression

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Examples – Point of View Find the Angle Elevation Find the Height of the boat from the sea floor.

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