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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 - ___
Answer key and some notes:
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 - 3√3 - 6 b. 2 - 2√3 - 4 c. √ 2 -
√ 6 - 2√ 2 d.
2.5 - 2.5√3 -
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.
