# Mostly Considered As Equilateral Isosceles Essay

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## Question:

Discuss About The Mostly Considered As Equilateral Isosceles.

### 1. What is a 30 60 90 Triangle?

In geometry there is a presence of different varieties of triangles that can be classified into several names according to different forms of classification. Some of the triangles can be classified with the help of their side length. These are mostly considered as the equilateral, isosceles and scalene triangles. Some of the triangles can again be measured with the angles they possess. For example the right angles, the obtuse angles and the acute angles. There are even subdivisions of these classification of the triangles. The triangles can also be classified into several smaller groups but in this following section it is going to be discussed about a special kind of a right triangle which has only one right angle, or a 90 degree angle. This particular kind of triangle is known as a 30 60 90 triangle which is nothing but a right angle triangle where one angle is 90 degrees and the other two angles are consecutively 60 and 30 degrees. There is no common order of occurrence for the angles and they can occur randomly. The 30 60 90 triangle is an important triangle in geometry as it has specific relationship with the sides it possesses. it is a geometrical fact that the hypotenuse in a right angle triangle can be considered as the longest side, and in a 30 60 90 triangle the hypotenuse is exactly the opposite side of the 90 degree angle directly across. In a 30 60 90 triangle it is easier to measure any of the three sides by understanding the length of at least one side of the triangle. It can be easily seen with general geometric calculations from the basic level that the hypotenuse is double the size of the shorter side which is usually across the 30 degree angle. Again it has been found in the 30 60 90 triangle that the hypotenuse is equal to the shorter leg twice by its value and the longer leg is a cross the 60 degree angle. The measurement of the longer angle is usually measured by multiplying the shorter leg with the square root of 3. The short leg usually served as the connecting bridge between two sides of the triangle. The measurement of the longer leg to the hypotenuse all vice-a-versa can easily be obtained but if it passes through the short leg the value can be easily found. Power it is also we found that there is no direct route from the longer led to the hypotenuse or the hypotenuse to the longest leg.

### 2. Why It Works: 30 60 90 Triangle Theorem Proof

The theorem of 30 60 90 triangle states that in a particular 30 60 90 triangle the sides are in the ratio 1: 2:?3.

### The proof of the theorem would be provided as below:

It needs to be proved that the 30 60 90 triangles have the sides in the ratio of 1: 2:?3. therefore for this proof it is required to keep in mind that the smallest site one needs to be the opposite of the smallest angle 30° which is the basic rule of a 30 60 90 triangle. On the other hand decide to would have to be larger than ?3 and 1: 2:?3 has the corresponding value of the 30 60 90 triangle which finds it easier to remember the sequence of 1: 2:?3.

For answering the problem regarding the 30 60 90 triangle as mentioned above, its needs to be considered that an equilateral triangle ABC is drawn. Then it needs to be specified that each of the equal angles are 60 degrees. Then a straight line is drawn bisecting it into to 30 degree angles and this line is called AD. AD is perpendicular bisector of BC.

On the other hand the triangle ABD therefore is now a 30 60 90 triangle and the triangle ADC is also 30 60 90 triangle. Therefore it implies that BD is equal to BC and BD is half of BC. On the other hand it also implies that BD is half of AB since AB is equal to BC. Therefore with this it can be proved AB: BD = 2:1.

Taking the Pythagorean Theorem. it can clearly be said that the measurement of the third side, which is AD, can be found.

AD2 = 4 ? 1 = ? 3