Difference between revisions of "30-60-90 triangle"
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A '''30-60-90''' triangle is a right triangle with a 30 degree angle, a 60 degree angle,a 90 degree angle. It is special because it side lengths are always in the same ratio. The length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is <math>\sqrt{3}</math> the length of the shorter leg. | A '''30-60-90''' triangle is a right triangle with a 30 degree angle, a 60 degree angle,a 90 degree angle. It is special because it side lengths are always in the same ratio. The length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is <math>\sqrt{3}</math> the length of the shorter leg. | ||
| − | Simply put, the ratio in order of the sides opposite to the angles for any value of <math> | + | Simply put, the ratio in order of the sides opposite to the angles for any value of <math>y</math> is <math>y</math> : <math>y</math><math>\sqrt{3}</math> : <math>2y</math>. It is a simple "pneumonic" ratio that will help you remember the ratio and each ratio corresponds to the ratio of the 30-60-90 triangle. |
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| + | [[Image:30-60-902.PNG|center]] | ||
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==Proof (using trig)== | ==Proof (using trig)== | ||
{{stub}} | {{stub}} | ||
Revision as of 22:48, 3 January 2025
A 30-60-90 triangle is a right triangle with a 30 degree angle, a 60 degree angle,a 90 degree angle. It is special because it side lengths are always in the same ratio. The length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is 
the length of the shorter leg.
Simply put, the ratio in order of the sides opposite to the angles for any value of 
is : : 
. It is a simple "pneumonic" ratio that will help you remember the ratio and each ratio corresponds to the ratio of the 30-60-90 triangle.
Proof (using trig)
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