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Understanding Special Right Triangles: Calculating Side Lengths and Values

This resource provides a comprehensive overview of the properties and calculations related to special right triangles, specifically 45-45-90 and 30-60-90 triangles. It includes essential theorems that help determine the lengths of sides and the hypotenuse based on given values. With clear examples and practice problems, learners can find the variable lengths and areas of triangles while ensuring their answers are in the simplest radical form. Ideal for students seeking to master right triangle fundamentals.

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Understanding Special Right Triangles: Calculating Side Lengths and Values

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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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