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Calculating Variables in Special Right Triangles Using Properties

Explore the properties of 45-45-90 and 30-60-90 right triangles to find unknown variables. This resource covers key theorems, including how to calculate the hypotenuse and leg lengths based on given sides. Specific focus is given to practice problems where you must find the value of x in simple radical form, calculate triangle areas, and fill in tables for side lengths. Perfect for students looking to strengthen their understanding of special right triangles in geometry.

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Calculating Variables in Special Right Triangles Using Properties

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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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