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+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 - Converse Can this form a triangle? Prove it: Show the work!

Pythagorean Theorem and Its Converse 𝑎 2 + 𝑏 2 = 𝑐 2 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? . 3. 4.

Pythagorean Triple A set of nonzero whole numbers a, b, and c that satisfy the equation 𝑎 2 + 𝑏 2 = 𝑐 2 Common Triples 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 They can also be multiples of the common triples such as: 6, 8, 10 9, 12, 15 15, 20, 25 14, 28, 50

Special Right Triangles Section 8.2 Special Right Triangles

Special Right Triangles 45°-45°-90° x 𝑥 2 x 45° 90° x 𝑥 2

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

Special Right Triangles 30°-60°-90° 𝑥 3 2x x 30° 60° 90° x 𝑥 3 2x

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

Right Triangle Trigonometry Section 8.3 Right Triangle Trigonometry

Trigonometric Ratios Sine = Opposite Hypotenuse Cosine = Adjacent Tangent = Opposite Adjacent sin 𝑂 𝐻 cos 𝐴 𝐻 tan 𝑂 𝐴

SOHCAHTOA Remember this 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: When you have the angle you would use: sin cos tan When you need the angle you would use: sin −1 cos −1 tan −1

Examples Solve for the missing variable Solve for the missing variable

Examples Solve for the missing variable Solve for the missing variable

Examples Find m< A and m< B

Examples Solve for the missing variables

Angle of Elevation and Angle of Depression 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.