Presentation on theme: "Unit 2 - Right Triangles and Trigonometry"— Presentation transcript:
1 Unit 2 - Right Triangles and Trigonometry Chapter 8
2 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, 7Since > > > 6 it is a triangleExample: 1, 2, 3Since 1+2 = > > 2 it is not a triangle!
3 Examples - Converse Can this form a triangle? Prove it: Show the work!
4 Pythagorean Theorem and Its Converse 𝑎 2 + 𝑏 2 = 𝑐 2cabConverse of the Pythagorean Theoremc2 < a2 + b2 then Acutec2 = a2 + b2 then Rightc2 > a2 + b2 then Obtuse
6 Pythagorean TripleA set of nonzero whole numbers a, b, and c that satisfy the equation 𝑎 2 + 𝑏 2 = 𝑐 2Common Triples3, 4, 55, 12, 138, 15, 177, 24, 25They can also be multiples of the common triples such as:6, 8, 109, 12, 1515, 20, 2514, 28, 50
7 Special Right Triangles Section 8.2Special Right Triangles
8 Special Right Triangles 45°-45°-90°x 𝑥 2x45°90°x𝑥 2
9 Examples – Solve for the Missing Sides Solve or x and ySolve for e and f
10 Special Right Triangles 30°-60°-90°𝑥 xx30°60°90°x𝑥 32x
11 Examples – Solve for the Missing Sides Solve for x and ySolve for x and y
12 Right Triangle Trigonometry Section 8.3Right Triangle Trigonometry
13 Trigonometric Ratios Sine = Opposite Hypotenuse Cosine = Adjacent Tangent = Opposite Adjacentsin 𝑂 𝐻 cos 𝐴 𝐻 tan 𝑂 𝐴
14 SOHCAHTOA Remember this SOHCAHTOA Remember this!!!! Write this on the top of your paper on all tests and homework!