Question

any one can explain 30 60 90 theoram

Answer 1

it is a theorem of angles of a triangle .
it is also known as angle sum property.
if one angle is 30 second is 60 then third will be 90

Answer 2

A 30-60-90 triangle is special because of the relationship of its sides. Hopefully, you remember that the hypotenuse in a right triangle is the longest side, which is also directly across from the 90 degree angle. It turns out that in a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.

The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle. The longer leg, which is across from the 60 degree angle, is equal to multiplying the shorter leg by the square root of 3. This picture shows this relationship with x representing the shorter leg.

Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:

Shorter leg ---> Longer Leg: Multiply by square root of 3
Longer leg ---> Shorter Leg: Divide by square root of 3
Shorter Leg ---> Hypotenuse: Multiply by 2
Hypotenuse ---> Shorter Leg: Divide by 2

Notice that the shorter leg serves as a bridge between the other two sides of the triangle. You can get from the longer leg to the hypotenuse, or vice versa, but you first 'pass through' the shorter leg by finding its value. In other words, there is no direct route from the longer leg to the hypotenuse, or vice versa.