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Special Right Triangles

Explore concepts of special right triangles including 45º-45º-90º and 30º-60º-90º triangles. Learn to calculate hypotenuse lengths, leg ratios, and solve related problems with radical expressions.

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Special Right Triangles

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  1. Special Right Triangles Advanced Geometry Trigonometry Lesson 2

  2. radical – the sign that indicates a root is to be taken radical expression – an expression containing a radical

  3. Special Right Triangles 45º- 45º- 90º Triangles In a 45º-45º-90º triangle, the length of the hypotenuse is times the length of a leg. hypotenuse n leg n A 45º-45º-90º triangle is also known as an isosceles right triangle. n leg

  4. Examples: Find x and y.

  5. Example: The length of a diagonal of a square is 6 meters. Find the perimeter of the square.

  6. 30º- 60º- 90º Triangles In a 30º-60º-90º triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is times the length of the shorter leg. hypotenuse 2n n long leg n short leg

  7. Examples:

  8. Example:

  9. Example: The length of the altitude of an equilateral triangle is 6 feet. Find the length of a side of the triangle.

  10. Example: Find x, y, and z.

  11. Example: Triangle RST is a 30°-60°-90° triangle with right angle RST. is the shorter leg with endpoints S(1, 1) and T(4, 1). Locate point R in quadrant IV.

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