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Chapter 8: Right Triangles and Trigonometry

Chapter 8: Right Triangles and Trigonometry. Section 8-2: Special Right Triangles. Objectives:. To use properties of 45º-45º-90º triangles. To use properties of 30º-60º-90º triangles. Theorem 8-5: “45º-45º-90º Triangle Theorem”.

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Chapter 8: Right Triangles and Trigonometry

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  1. Chapter 8:Right Triangles and Trigonometry Section 8-2: Special Right Triangles

  2. Objectives: • To use properties of 45º-45º-90º triangles. • To use properties of 30º-60º-90º triangles.

  3. Theorem 8-5:“45º-45º-90º Triangle Theorem” • In a 45º-45º-90º triangle, both legs are congruent and the length of the hypotenuse is the leg times the square root of 2.

  4. Example • Solve for the variables. y 6 x

  5. Example • Solve for the variables. x y 17

  6. Example • Solve for the variables. y x

  7. Example • Solve for the variables. 3 y x

  8. Example • Solve for the variables. y x

  9. Example • Solve for the variables. y x

  10. Example • A high school softball diamond is a perfect square. The distance from base to base is 60 ft. To the nearest foot, how far does Jean (the catcher) have to throw the ball to second base to throw out an attempted base stealer?

  11. Theorem 8-6:“30º-60º-90º Triangle Theorem” • In a 30º-60º-90º triangle, the length of the hypotenuse is twice the short leg. The length of the long leg is the square root of three times the short leg.

  12. Example • Solve for the variables. x y 4

  13. Example • Solve for the variables. y x

  14. Example • Solve for the variables. 28 x y

  15. Example • Solve for the variables. x y

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