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Aim: What’s so special about a 30 0 -60 0 -90 0 triangle?

60 0. 60 0. 60 0. 30 0. 30 0. 60 0. 60 0. 30 0. 30 0. Aim: What’s so special about a 30 0 -60 0 -90 0 triangle?. Do Now: Triangle ABC is equilateral with each side equal to 2 x. CD is an altitude of ABC. What is m A? m B? m ACB? What is m ACD? m BCD?.

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Aim: What’s so special about a 30 0 -60 0 -90 0 triangle?

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  1. 600 600 600 300 300 600 600 300 300 Aim: What’s so special about a 300-600-900 triangle? Do Now: Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC. What is mA? mB? mACB? What is mACD? mBCD? C 2x 2x A B D 2x

  2. x x x2 + (CD)2 = (2x)2 300-600-900 triangle Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC What is length of CD in terms of x? C 300 2x 2x Pythagorean Theorem - a2 + b2 = c2 ? 600 A B 2x D x2 + (CD)2 = 4x2 (CD)2 = 3x2

  3. 3 3 32 + (CD)2 = (6)2 300-600-900 triangle Triangle ABC is equilateral with each side equal to 6 (instead of 2x). CD is an altitude of ABC What is length of CD? C 300 Pythagorean Theorem - a2 + b2 = c2 6 6 ? 600 A B D 9 + (CD)2 = 36 (CD)2 = 27

  4. C 6 C 3 A D 3 3 2x x A D x 3 300-600-900 triangle Problem 1 Problem 2 300 300 600 600 Review the results of the first two problems. Can you make any general conclusions?

  5. 300-600-900 triangle 300 2s 600 s

  6. 450 x 450 2 2 x x2 + x2 = ( )2 2x2 = ( )2 45o - 45o - 90o triangle Do Now: Triangle ABC is an isosceles right triangle with BC = A. What is mB? mC? AB? AC? C A B Pythagorean Theorem - a2 + b2 = c2 2x2 = 8

  7. 6 6 x x 6 6 6 2 2 2 45o - 45o - 90o triangle Triangle ABC is an isosceles right triangle with BC = A. What AB? AC? Do Now: C A B Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = ( )2 2x2 = 72 x2 = 36 x = 6

  8. 2 6 2 6 300-600-900 triangle Problem 1 Problem 2 C C A B A B Review the results of the first two problems. Can you make any general conclusions?

  9. 450- 450 - 900 triangle In a 450-450-900 triangle, the length of the hypotenuse is times the length of a leg. 450 s 450 s Ratio of Hypotenuse : Leg of I.R.T is always

  10. = 1.4142 . . = = 1.4142 . . = = 1.4142 . . = = 1.4142 . . = EI CG DH BF 450 AE AD AB AC 450 2 2 2 2 Isosceles Right Triangle 450 – 450 - 900 triangle Ratio of Hypotenuse : Leg of I.R.T is always

  11. Summary of Special Angles in Trig

  12. AC = (AB) AC = (3.5) Longer leg is times the shorter leg 3 3 Model Problem Do Now: Triangle ABC is a 30-60-90 triangle with BC = 7 A. What is length of AB? AC? C 300 7 3.5 A B 600 3.5 Hypotenuse is 2 times the shorter leg CB = 2(AB) 7 = 2(AB) 3.5 = AB AC  6.06

  13. Ratio of Hypotenuse : Leg of I.R.T is always x Pythagorean Theorem - a2 + b2 = c2 Instead of x x2 + x2 = (8)2 2x2 = 64 x2 = 32 x = 32 x = 4 2 Model Problem Do Now: Triangle ABC is an isosceles right triangle with BC = 8 A. What AB? AC? C 8 A B

  14. Regents Prep What is the exact sum of + 0

  15. h 6 in. x 600 600 Longer leg is times the shorter leg A = bh = 6( ) = 31.2 in2 h = Model Problem The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel? A = bh Draw an altitude of the rhombus. Label x and has shown 6 in. 6 in. Hypotenuse is 2 times the shorter leg 6 = 2x 3 = x

  16. hypotenuse is times the length of a leg.  90 = 127.27922’ 2 2 Model Problem A baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does the second baseman throw a ball to home plate? 90’ Isosceles Right Triangle 90’

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