## Friday, May 25, 2012

### Special Right Triangles: 30-60-90 and 45-45-90 Degrees Right Triangles

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Thanks a lot!!  Mrs. Lin

These are the two most common right triangles.

For 45-45-90 degrees, the ratio is  1 - 1 - √ 2

For 30-60-90 degrees, the ratio is  1 - √ 3 - 2

Other concepts to remember are that in any triangle a. larger angle corresponds to longer side and b.same
angles have the same side length.

Level 0 skills check practices:

Find the missing side length (answers below)

I: 45-45-90 degrees right triangle

a. 3 - ___- ___            b. 5 - ___- ___         c.   2 - ___ - ___      d. tricky : ___ - ___ - 3

e. ___ - ___ - 4           f. ___ - ___ - 6

II. 30-60-90 degrees right triangle

a. 3 - ___- ___            b.  ___- ___  - 4        c.   2 - ___ - ___      d. ___ - ___ - 5

e.  ___ - 6 - ___           f. ___ - 3 - ___

I: 45-45-90 degrees right triangle

a. 3 - 3- 3  2              b. 5 - 5 - 5  2         c.   2 -  2  - 2       d. 6 /2 - 6 /2 - √3

e. 2√ 2 - 2√ 2 - 4         f. 3 2 - 3√ 2  - 6

Notes:
a. Given the side length to 45 degrees, the easiest way to get the 90 degree side length is to time that number by  2 .

b. Given the side length to 90 degrees, the easiest way to get the 45 degree side length is to divide that number by 2 and then times  2 .

II. 30-60-90 degrees right triangle

a. 3 - 33 - 6            b.  2 - 2√3 - 4        c.   2 6  - 2√ 2       d. 2.5 - 2.53 - 5

e.  2√3 - 6 - 4√3         f.  3 - 3 -  2√3

Notes:
a. Given the side length to 30 degrees, the easiest way to get 90 degrees side length is to times 2 to the 30 degree side length. To get the side length to 60 degrees, times 3 to the side length to 30 degrees.

b. Given the side length to 90 degrees, divide 90 degree side length by 2 to get the side length to 30 degrees.Times 3 to the side length of 30 degrees to get the side length of 60 degrees.

c. Given the side length to 60  degrees, divide that number by 3 and then times 3  to get the side length of 30 degrees. Times 2 to get the side length of 90 degrees.