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Special Right Triangles: Difference between revisions

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==45-45-90 Special Right Triangles==
==45-45-90 Triangles==


This concept can be used with any [[right triangle]] that has two <math>45^\circ</math> angles.
{{main|45-45-90 triangle}}
This concept can be used with any [[right triangle]] that has two <math>45^\circ</math> angles. All 45-45-90 triangles are [[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\sqrt2</math>.


A 45-45-90 Triangle is always [[isosceles]], so let's call both legs of the triangle <math>x</math>.
==30-60-90 Triangles==


If that is the case, then the [[hypotenuse]] will always be <math>x\sqrt 2</math>.
{{main|30-60-90 triangle}}
A 30-60-90 triangle is a 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>. There is also the ratio of <math>1:\sqrt3:2</math>. With 2 as the hypotenuse and 1 opposite of the 30 degrees. That leaves <math>\sqrt3</math> as the only length left.


==30-60-90 Special Right Triangles==
==See Also==
 
* [[Pythagorean triple]]
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>.
 
There is also the ratio of <math>1:\sqrt3:2</math>. With 2 as the hypotenuse and 1 opposite of the 30 degrees. That leaves <math>\sqrt3</math> as the only length left.


==See Also==
{{stub}}
[[Pythagorean triple]]

Revision as of 17:11, 30 January 2025

45-45-90 Triangles

Main article: 45-45-90 triangle

This concept can be used with any right triangle that has two $45^\circ$ angles. All 45-45-90 triangles are isosceles, so let's call both legs of the triangle $x$. If that is the case, then the hypotenuse will always be $x\sqrt2$.

30-60-90 Triangles

Main article: 30-60-90 triangle

A 30-60-90 triangle is a right triangle that has a $30^\circ$ angle and a $60^\circ$ angle. Let's call the side opposite of the $30^\circ$ angle $x$. Then, the side opposite of the $60^\circ$ angle would have a length of $x\sqrt 3$. Finally, the hypotenuse of a 30-60-90 Triangle would have a length of $2x$. There is also the ratio of $1:\sqrt3:2$. With 2 as the hypotenuse and 1 opposite of the 30 degrees. That leaves $\sqrt3$ as the only length left.

See Also

This article is a stub. Help us out by expanding it.

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