Special right triangles

Hi Friends! In this answer math problems for free session we will discuss about Special right triangle. A special right triangle is a right triangle having specific characteristics which make its calculations much easier or for which simple formulas exist. We can classify special right triangles in two categories: the angles of a right triangle may form some simple relationships, such as 45–45–90. The right triangles in this category are “angle-based" right triangle. Another category is on the basis of sides of the triangle, when the lengths of the sides form some ratios, and then those triangles are called “side-based" right triangles.
There are four types of special right triangles:
These two types come under side based special right triangles:
3–4–5 Triangles:
A 3-4-5 triangle is a special right triangle whose lengths of the sides are in the ratio of 3:4:5. The ratios can only be checked when you are given the lengths of any two sides of the triangle.
5–12–13 Triangle:
A 5-12-13 triangle is a special right triangle whose lengths of the sides are in the ratio of 5:12:13.
These two types come under angle based special right triangle (get more detail here):
45º45º90º right triangles or isosceles right triangle: An isosceles right triangle is a triangle having the characteristic of both isosceles and the right triangle as it has two equal angles, two equal sides, and one right angle.  So the angles of an isosceles right triangle are 45°- 45°- 90°. Therefore the lengths of the sides of a 45°- 45°- 90° triangle are in the ratio of 1:1:√2.
A right angled triangle having two sides equal in length is called 45°- 45°- 90° triangle.
30º-60º-90º Triangles
A 30°- 60°- 90° right triangle is a special right triangle whose angles are 30°, 60°and 90° and therefore the lengths of the sides of a 30°- 60°- 90° triangle are in the ratio of 1:√3:2 .

In upcoming posts we will discuss about Planar cross-sections and Measures of central tendency in Grade XI. Visit our website for information on CBSE class 12 home science question bank

Rotations

In this answers to math problems session we are going to discuss about the different types of transformations of which one of is rotation but first of all we have to know about the meaning of transformation. According to one of the online tutor definition of transformation it is the way of changing the shape or appearance of the figure means how the size and shape effected of the figure when some transformation methods applied on that figure.
There are some ways for math transformations in which rotations is one of the method of transformation that is defined as follows .Rotation definition is any shape that means turning around the center , But there will be one thing is that at any point if we calculate the distance from the center is the same and also it can be understand as that each point will makes the circle around itself and that point is the center of that circle that is equal for every point of its circumference .It is the method of transformation through which the shape of the thing will not change but its orientation is changed . Useful resource for more information on rotations.
Rotation is the method in which the thing will be rotated at any of the point on that shape and the shape will not change for the point of rotation means only the orientation of the figure is changed or its side will be changed not its size .It is only move at the point that is becomes it center and all the other points of the center are on common distance. So the figure that are rotated from any point will change its facing side means if we want to change the face of the figure then we use the rotation method of transformation .

In upcoming posts we will discuss about Special right triangles and Methods of data representation. Visit our website for information on CBSE home science syllabus

Coordinate geometry

In mathematics the coordinate geometry have a great importance. So we are going to discuss here the coordinate geometry. To understand the coordinate geometry you should be familiar with some related terms of coordinate geometry. The grid is a combination of horizontal (Find Horizontal Asymptote) and vertical lines that makes the squares. On the grid squares two points are there called axis, the x- axis and y- axis, the x axis represents the horizontal line and y axis represents the vertical lines. Both the points are intersecting on some point that is O point and called the origin. In which we determine the distance between the two points or the simple definition of the coordinate geometry is that, it is used mainly to address the point that are on the plane by using numbers of pairs that should be in ordered form.
Coordinate geometry formulas are used to define some coordinate geometry topics.
To determine the distance between the two pints we use distance formula that is
Distance d = √ [(x_{2 –} x₁)² + (y_{2 –} y₁)² ],
To find the angle between the two lines, we have formula θ tan – ¹m, where ‘m’ is slope, an angle may be anyone like right, acute, obtuse etc.
The slope formula is m = (y₂ – y₁) / (x₂ – x₁), we can also find the slope for perpendicular and parallel lines.
The midpoint formula (x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2),
We can also find the area and perimeter of a polygon in the field of geometry that is defined by the points. We can also transform the shapes in the coordinate geometry. It is used mostly in real life constructions.


In upcoming posts we will discuss about Rotations and Statistical experiments. Visit our website for information on CBSE previous years 11 physics

reflections

In this math helper blog we are going to discuss about the different types of laplace transformations in which one is reflections but first of all we have to know about the meaning of transformation that, it is defined as any change in the shape, size or orientation of the thing and According to the definition of transformation it is the way of changing the shape or appearance of the figure is known as the transformation of the figure. One of the methods of transformation is reflections that are defined as follows.
Reflection: It is also one of the methods of transformation in which mirror image of the things will created. In the reflection always side of the thing will changed means it will appear on its opposite side and also the shape of that thing will not change. One more thing should be noted that if we define reflection mirror image of the particular thing will make on the same line as original thing and also on the same line on which actual thing is situated. A mirror line either horizontal or vertical it will not change the shape of the thing .So according to the reflection definition when applied a method that provide the mirror image of the figure is known as the reflection that is the one of method of transformation . For more details for reflection click here
There are many example of reflection that are as echo of noise is one of the common example of daily life .Reflection is used in many technologies as SONAR, radar etc. All the waves as radio waves or electromagnetic waves are work on the method of reflection .So the reflection will give the many of the important application that is mostly used in our life.

In upcoming posts we will discuss about Coordinate geometry and Correlation and causation. Visit our website for information on CBSE political science board paper

trigonometric ratios

Hello students, in this blog we are going to discuss the trigonometric ratios. The trigonometric ratios of angles are used to find the angles and sides for a triangle when we have some of angles and sides are given. This task is the main task of the trigonometric ratios. This problem is solved by using some ratios of the sides of a triangle with respects to its acute angles. These ratios of acute angles (What is an Acute Angle) are called the trigonometric ratios of angles.
Note: - The trigonometric ratios are same for the same length.
We have six trigonometric ratios; let’s take a look on them.
With reference to an angle ‘A’ in a right angled, ΔABC, right angled at ‘c’.
‘a’ is the opposite side (Perpendicular)
‘b’ is the adjacent side (Base)
‘c’ is the hypotenuse.
The ratios of sides a / c, b / c, a / b, b / a, c / b, c / a have the following names, they are : -
a / c is called the sine of ‘A’, written as sin A.
b / c is called the co-sine of ‘A’, written as cos A.
a / b is called the tangent of ‘A’, written as tan A.
b / a is called the co-tangent of ‘A’, written as cot A.
c / b is called the secant of ‘A’, written as sec A.
c / a is called the co-secant of ‘A’, written as cosec A.
Thus, we have six trigonometrically ratios which must be memorized
sin A = perpendicular / hypotenuse,
cos A = base / hypotenuse,
tan A = perpendicular / base,
cosec A = hypotenuse / perpendicular,
sec A = hypotenuse / base,
cot A = base / perpendicular,


In upcoming posts we will discuss about reflections and Permutations and combinations. Visit our website for information on business studies class 12 CBSE syllabus

circles

Circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point is always constant. This fixed point is called center of circle. Practice on circles by Finding the Area of a Circle
 Circles geometry can be explained as shown below,
A line segment joining the end point on the circle is called its radius. The plural of radius is radii.
A chord of a circle is a line segment joining any two points on the circle.
A diameter is a chord of circle passing through the center of circle.
The perimeter of a circle is called its circumference.
A line which intersects a circle in two distinct points is called a secant of the circle.
Theorem used in circles geometry is shown below,
Theorem: Equal chords of a circle subtend equal angle.
Given a circle C (O, r) in which chord AB = chord CD. To Prove that AOB = COD, we have OA = OC.
Sector of circle is enclosed by an arc of a circle and the two bounding radii. The diameter of circle divides the circle into two equal arcs; each of these two arcs is called a semicircle.
Circles which have the same center and different radii are called concentric circles (for more on circle click this). The different places of the circle are discussed below:
1. inside the circle
2. on the circle
3. outside the circle
Some other properties of circles,
The angle in the semicircle is a right angle which is 90°.
The arc of the circle subtends a rights angle at any point on the circle.
Angles in the same segment of a circle are equal.
Above discussion is helpful for Grade XII students to understand the concept of Circles.


In upcoming posts we will discuss about trigonometric ratios and Math Blog on Grade XI . Visit our website for information on CBSE syllabus for class xi english core