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Warm Up

Warm Up. Find the value of x. Leave your answer in simplest radical form. x. x. 7. 9. 7. 9. 7.3: Special Right Triangles. Objectives: To use the properties of 45-45-90 and 30-60-90 right triangles. 45°-45°-90° Right Triangle.

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Warm Up

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  1. Warm Up Find the value of x. Leave your answer in simplest radical form. x x 7 9 7 9

  2. 7.3: Special Right Triangles Objectives: To use the properties of 45-45-90 and 30-60-90 right triangles

  3. 45°-45°-90° Right Triangle It is an isosceles, right triangle– Both legs are congruent!! THEOREM: The hypotenuse is times the length of the legs IF YOU NEED TO FIND THE HYPOTENUSE: Hypotenuse = (Length of Leg) X IF YOU NEED TO FIND A LEG: Length of leg =

  4. Examples: • Find h: 2. Find x: h x 9

  5. Find x: x

  6. Find x: 1. 2. 6 x x

  7. Find x: x 10

  8. A square has a perimeter of 24 inches. How long is the diagonal?

  9. 30°-60°-90° Right Triangle • Shorter Leg is the side opposite the 30° angle • Longer leg is the side opposite the 60° angle Let the shorter leg = n HYPOTENUSE = 2 ∙ SHORTER LEG = 2n LONGER LEG = SHORTER LEG = n

  10. If you need to find the shorter leg (side opposite 30°): If given the hypotenuse: SHORTER LEG = If given the longer leg: SHORTER LEG=

  11. Fill in the table of values for the side lengths of a 30-60-90 triangle:

  12. Find the missing lengths. 1. 2. 60 g f y x 30 5

  13. Find the variables. 1. 2. 60 60 x k 4 m 30 y 30

  14. Find the value of each variable.(Figure not drawn to scale) b a 30 45 d c

  15. Find the value of each variable. Leave your answer in simplest radical form. 4 a 45° b

  16. Find the area. Round your answer to the nearest tenth. 60 60

  17. Find the area of the triangle. 45

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