Unit 2 Right Triangles and Trigonometry Chapter 8

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

Examples - Converse �Can this form a triangle? �Prove it: Show the work! �Can this form a triangle? �Prove it: Show the Work!

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

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

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

Section 8. 2 SPECIAL RIGHT TRIANGLES

Special Right Triangles � 45° 90° x x

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

Special Right Triangles � 30° 60° 90° x 2 x

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

Section 8. 3 RIGHT TRIANGLE TRIGONOMETRY

Trigonometric Ratios �Sine = 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 problem �Sin �Cos �Tan

Set up the problem �Sin �Cos �Tan

Trigonometric Ratios: � �

Examples �Solve for the missing variable

Examples �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.