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

2+3 > 1 3+1 > 2

Examples - Converse  Can this form a triangle?

 Can this form a triangle?

 Prove it: Show the work!

 Prove it: Show the Work!

Pythagorean Theorem and Its Converse   Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2  Converse of the Pythagorean Theorem  c 2 < a 2 + b 2 then Acute c a  c 2 = a 2 + b 2 then Right b  c 2 > a 2 Obtuse + b 2 then

1.

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Examples – What type of triangle am I?

3.

4.

2.

.

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

Section 8.2

SPECIAL RIGHT TRIANGLES

Special Right Triangles 

45°-45°-90°

45° 45° 90°

x 𝑥 2 x

x 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°

30° 60° 90°

𝑥 3 2x

x

𝑥 3

2x

x

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

Section 8.3

RIGHT TRIANGLE TRIGONOMETRY

Trigonometric Ratios  Sine = Opposite Hypotenuse  𝑂 sin 𝐻 𝐴 cos 𝐻 tan 𝑂 𝐴  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    Sin Cos Tan

Set up the problem    Sin Cos Tan

Trigonometric Ratios:  When you have the angle you would use:  When you need the angle you would use:  sin  cos  tan    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

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.