Art of Problem Solving

Special Right Triangles: Difference between revisions

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==45-45-90 Special Right Triangles==
#REDIRECT [[Special right triangles]]
 
This concept can be used with any [[right triangle]] that has two <math>45^\circ</math> angles.
 
A 45-45-90 Triangle is always [[isosceles]], so let's call both legs of the triangle <math>x</math>.
 
If that is the case, then the [[hypotenuse]] will always be <math>x\sqrt 2</math>.
 
==30-60-90 Special Right Triangles==
 
30-60-90 Triangles are special triangles where there is a certain ratio for the sides of the right triangle, as explained below.
 
This concept can be used for any right triangle that has a <math>30^\circ</math> angle and a <math>60^\circ</math> angle.
 
Let's call the side opposite of the <math>30^\circ</math> angle <math>x</math>.
 
Then, the side opposite of the <math>60^\circ</math> angle would have a length of <math>x\sqrt 3</math>.
 
Finally, the hypotenuse of a 30-60-90 Triangle would have a length of <math>2x</math>.
 
==See Also==
[[Pythagorean triple]]

Latest revision as of 14:54, 31 January 2025