8-8 Special Right Triangles and Trigonometry notes

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Mrs. Aitken’s Integrated 2Unit 8 Similar and Congruent TrianglesSide-noteThree ways to solve for an unknown side.• Special right triangle relationships (30-60-90, 45-45-90 triangles)• Pythagorean theorem (unless only one side is known)• Trig Ratios (sin, cos, tan)“SOHCAHTOA”Trigonometric ratios for special right triangles30º angle45º angle60º anglesin =oppositehypotenuseb 1=2b 2a 1=a 2 2b 3 3=2b 2cos =adjacenthypotenuseb 3 3=2b 2a 1=a 2 2b 1=2b 2tan = oppositeadjacentb 1=b 3 3a =1ab 3 = 3bSide noteDon’t rely on the table. Be able to use Pythagorean Theorem, trig ratios, and the specialright angle relations to find angle and/or side measures.Example 3Find the value of each variable.a. sin xº =32Think, which Δ contains √3? 30° - 60° - 90° Δ. So, x = 60°b. cos yº =32Think, which Δ contains √3? 30° - 60° - 90° Δ. So, y = 30°c. tan zº = 1 z = 45°The value of a trig ratio depends only on the measure of the angle, not on the size of thetriangle.8-8 Special Right Triangles and Trigonometry
Mrs. Aitken’s Integrated 2Unit 8 Similar and Congruent TrianglesExample 4: Find the value of the variable.a. b.Solution 4a. 30° - 60° - 90° Δ b. 45° - 45° - 90° Δ
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8-8 Special Right Triangles and Trigonometry notes

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