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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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