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30 60 90 Triangles

Top30 60 90 Triangles are triangles with angles of measure 30, 60 and 90 degrees. In these types of triangles sides are in the Ratio of the 1 : 2 : √3. If we divide an Equilateral Triangle into two equal parts then we get these types of right angled triangle.

For right triangles we use Trigonometric Functions for calculation of sides and angles but for this special type length ratio is used for calculations. Special feature of this triangle is that length of the sides of triangle follow a special trend. Suppose short leg which is opposite to the angle 30 degree has length 'y' and hypotenuse has length of 2y. So long leg is opposite to angle 60 degree has length √3y.

With help of these ratios we can calculate length of sides of this Right Triangle.
Suppose in a 30 60 90 degree triangle length of shortest leg is 20 then length of other sides can be calculated as shown below.

We know that hypotenuse of such triangle is twice the shortest leg and longest leg is √3 times of shortest leg. So with help of this property we can solve this problem.
Here hypotenuse will be 2 * 20 = 40.
And the longest leg is = 20 √3.
In a 30 60 90 degree Right Angle triangle we have the length of the shortest leg which is 8. Find the length of other sides?
We know that hypotenuse of such triangle is twice the shortest leg and longest leg is √3 times of shortest leg.
Here hypotenuse will be 2 * 8= 16.
And longest leg is = 8√3.