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

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

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**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

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**Examples – What type of triangle am I?**

. 3. 4.

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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

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**Special Right Triangles**

Section 8.2 Special Right Triangles

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**Special Right Triangles**

45°-45°-90° x 𝑥 2 x 45° 90° x 𝑥 2

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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° 𝑥 x x 30° 60° 90° x 𝑥 3 2x

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**Examples – Solve for the Missing Sides**

Solve for x and y Solve for x and y

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**Right Triangle Trigonometry**

Section 8.3 Right Triangle Trigonometry

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**Trigonometric Ratios Sine = Opposite Hypotenuse Cosine = Adjacent**

Tangent = Opposite Adjacent sin 𝑂 𝐻 cos 𝐴 𝐻 tan 𝑂 𝐴

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**SOHCAHTOA Remember this**

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

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Set up the problem Sin Cos Tan

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**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

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Examples Solve for the missing variable Solve for the missing variable

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Examples Solve for the missing variable Solve for the missing variable

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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 Angle of Elevation and Angle of Depression

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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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Geometry Notes Lesson 5.3A – Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles.

Geometry Notes Lesson 5.3A – Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles.

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