8-8 Special Right Triangles and Trigonometry notes

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Mrs. Aitken’s Integrated 2Unit 8 Similar and Congruent TrianglesIn a 30º-60º-90º triangle, the measure of the hypotenuse is twice the measureof the shorter leg. The measure of the longer leg is √3 times the measure ofthe shorter leg.Notice: the shorter leg is the leg connecting the 60°and 90° angles.Example 1Find the approximate measure of each unknown side in each triangle.a.SolutionXY =a√2 = 2 and XZ = ZY = aso XY = XZ(√2) now solve for XZ2 = XZ(√2)2= 1.4 so XZ = ZY = 1.42b. SolutionJK = 12 ← Hypotenuse (2b)JL ← shorter leg ( b), so 1 • JK = 1 • 12 = 62 2KL ← longer leg (b√3), so ( JL ) 3 = 6 3 ≈10.48-8 Special Right Triangles and Trigonometry
Mrs. Aitken’s Integrated 2Unit 8 Similar and Congruent TrianglesExample 2Find the measure of the unknown sides.a. b. c.Solutiona. 45° - 45° - 90° Δ because it is an isosceles right triangle.SR ← leg = a = 10TR ← leg = a = 10ST ← hypotenuse = a√2ST = 10√2≈ 14.14b. 45° - 45° - 90° ΔPN ← hypotenuse =a√2 = 9√2So, a = 9PM ← leg = a = 9NM ← leg = a = 9c. 30° - 60° - 90° ΔJL ← shorter leg = b = 5KL ← longer leg = b√3 = 5√3KJ ← hypotenuse = 2b = 10Trigonometric Ratiosmeasureof leg opposite∠ABCsin A ==measureof hypotenuseABmeasure of leg adjacent to ∠ A ACcos A = =measure of hypotenuse ABmeasure of leg opposite ∠ A BCtan A = =measure o f leg adjacent to ∠AACBlegopposite‹AChypotenuseleg adjacent to ‹AA8-8 Special Right Triangles and Trigonometry
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8-8 Special Right Triangles and Trigonometry notes

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